%I A001469 M3041 N1233
%S A001469 1,1,3,17,155,2073,38227,929569,28820619,1109652905,51943281731,
%T A001469 2905151042481,191329672483963,14655626154768697,1291885088448017715,
%U A001469 129848163681107301953,14761446733784164001387
%V A001469 -1,1,-3,17,-155,2073,-38227,929569,-28820619,1109652905,-51943281731,
%W A001469 2905151042481,-191329672483963,14655626154768697,-1291885088448017715,
%X A001469 129848163681107301953,-14761446733784164001387
%N A001469 Genocchi numbers (of first kind); unsigned coefficients give expansion of tan(x/2).
%D A001469 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 49.
%D A001469 D. Dumont, Interpretations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
%D A001469 A. Fletcher, J. C. P. Miller, L. Rosenhead, and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2\
, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
%D A001469 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 528.
%D A001469 J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23.
%D A001469 G. Kreweras, Sur les permutations compte'es par les nombres de Genocchi..., Europ. J. Comb., vol. 18, pp. 49\
-58, 1997.
%D A001469 D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Annals Math., 36 (1935), \
637-649.
%D A001469 H. M. Terrill and E. M. Terrill, Tables of numbers related to the tangent coefficients, J. Franklin Inst., 2\
39 (1945), 64-67.
%D A001469 Review of Terrill-Terrill paper, Math. Comp., 1 (1945), p. 386.
%D A001469 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.8.
%H A001469 E. W. Weisstein, Link to a section of The World of Mathematics.
%H A001469 Index entries for sequences related to Bernoulli numbers.
%F A001469 a(n) = 2*(1-4^n)*B_{2n} (B = Bernoulli numbers).
%F A001469 x tan (x/2) = Sum x^n*|a(n)|/(2n)!; n >= 1.
%e A001469 tan(x/2) = 1/2*x + 1/24*x^3 + 1/240*x^5 + 17/40320*x^7 + 31/725760*x^9 + O(x^11)
%Y A001469 Cf. A006846.
%K A001469 sign,done,easy,nice,huge
%O A001469 1,3
%A A001469 njas
%E A001469 More terms from James A. Sellers (sellersj@math.psu.edu), Jul 06 2000
#######################################################################################################################
a(n) = 2*(1-4^n)*B_{2n}
#######################################################################################################################
Computed by Simon Plouffe , may 2002.
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
2, 1
4, 1
6, ``(3)
8, ``(17)
10, ``(5)*``(31)
12, ``(3)*``(691)
14, ``(7)*``(43)*``(127)
16, ``(257)*``(3617)
18, ``(3)^2*``(73)*``(43867)
20, ``(5)*``(31)*``(41)*``(283)*``(617)
22, ``(11)*``(89)*``(131)*``(593)*``(683)
24, ``(3)*``(17)*``(103)*``(241)*``(2294797)
26, ``(13)*``(657931)*``(8191)*``(2731)
28, ``(7)*``(43)*``(113)*``(127)*``(362903)*``(9349)
30, ``(3)*``(5)*``(151)*``(331)*``(1001259881)*``(1721)
32, ``(37)*``(257)*``(683)*``(65537)*``(305065927)
34, ``(17)*``(151628697551)*``(131071)*``(43691)
36, ``(3)^2*``(73)*``(109)*``(26315271553053477373)
38, ``(19)*``(154210205991661)*``(174763)*``(524287)
40, ``(5)*``(17)*``(31)*_c21_1*``(61681)
42, ``(3)*``(7)*``(127)*``(337)*``(1520097643918070802691)*``(5419)
44, ``(11)*``(59)*``(89)*``(397)*``(683)*``(1798482437)*``(8089)*``(2947939)*``(2113)
46, ``(23)*_c23_1*``(2796203)*``(178481)
48, ``(3)*``(97)*``(241)*``(257)*``(653)*``(673)*``(153289748932447906241)*``(56039)
50, ``(5)^2*``(31)*``(251)*``(601)*_c26_1*``(4051)*``(1801)
52, ``(13)*``(157)*``(577)*``(1613)*_c22_1*``(58741)*``(8191)*``(2731)
54, ``(3)^3*``(73)*_c27_1*``(39409)*``(87211)*``(262657)
56, ``(7)*``(17)*``(43)*``(113)*``(127)*``(19088082706840550550313)*``(163979)*``(15790321)*``(113161)
58, ``(29)*``(67)*``(233)*``(1103)*_c33_1*``(186707)*``(2089)
60, ``(3)*``(5)*``(41)*``(151)*``(331)*``(1321)*_c39_1*``(2003)
62, ``(31)*``(157)*_c28_1*``(266689)*``(715827883)*``(2147483647)
64, ``(257)*``(641)*_c48_1*``(65537)
66, ``(3)*``(11)*``(89)*``(683)*``(839)*``(159562251828620181390358590156239282938769)*``(599479)*``(20857)
68, ``(17)*``(37)*``(101)*``(137)*``(953)*_c40_1*``(131071)*``(43691)*``(26317)
70, ``(5)*``(7)*``(31)*``(43)*``(127)*``(281)*_c41_1*``(86171)*``(688531)*``(122921)
72, ``(3)^2*``(17)*``(109)*``(241)*``(433)*_c55_1*``(38737)
74, ``(37)*``(223)*_c56_1*``(616318177)*``(1777)
76, ``(19)*``(229)*``(457)*_c53_1*``(58231)*``(174763)*``(524287)
78, ``(3)*``(13)*_c63_1*``(121369)*``(8191)*``(2731)
80, ``(5)*``(31)*``(257)*``(631)*_c64_1*``(10589)*``(61681)
82, ``(41)*_c69_1*``(38189)*``(13367)*``(4003)
84, ``(3)*``(7)*``(113)*``(127)*``(233)*``(271)*``(337)*``(1429)*_c57_1*``(68767)*``(5419)*``(14449)
86, ``(43)*``(431)*``(541)*_c73_1*``(21563)*``(9719)
88, ``(11)*``(17)*``(307)*``(353)*``(397)*``(683)*_c76_1*``(2113)
90, ``(3)^2*``(5)*``(73)*``(151)*``(331)*``(587)*``(631)*_c69_2*``(23311)*``(18837001)
92, ``(23)*``(277)*``(587)*``(1013)*``(1657)*_c68_1*``(2796203)*``(178481)*``(30269)
94, ``(47)*``(283)*``(467)*``(1499)*_c76_2*``(13264529)*``(2351)*``(4513)
96, ``(3)*``(193)*``(241)*``(257)*``(673)*_c88_1*``(65537)
98, ``(7)^2*``(43)*``(127)*_c88_2*``(1671211)*``(3221)*``(2857)
100, ``(5)^2*``(31)*``(41)*``(251)*``(263)*``(379)*``(601)*_c78_1*``(268501)*``(8101)*``(4051)*``(1801)
102, ``(3)*``(17)*``(59)*``(307)*``(827)*_c79_1*``(131071)*``(43691)*``(11119)*``(2143)*``(2857)*``(6529)
104, ``(13)*``(17)*``(37)*``(157)*``(1613)*_c93_1*``(8191)*``(2731)*``(858001)
106, ``(53)*_c93_2*``(37217)*``(3967)*``(69431)*``(20394401)*``(6361)
108, ``(3)^3*``(73)*_c97_1*``(87211)*``(279073)*``(262657)*``(246241)
110, ``(5)*``(11)*``(31)*``(89)*``(157)*``(683)*``(881)*_c94_1*``(76493)*``(3191)*``(201961)*``(2971)
112, ``(7)*``(43)*``(127)*``(257)*_c103_1*``(8065483)*``(15790321)*``(5153)
114, ``(3)*``(19)*``(571)*_c111_1*``(174763)*``(524287)*``(32377)
116, ``(29)*``(233)*``(1103)*_c120_1*``(7559)*``(2089)
118, ``(59)*_c122_1*``(179951)*``(37171)*``(2833)
120, ``(3)*``(5)*``(17)*``(151)*``(241)*``(331)*``(1321)*_c113_1*``(4562284561)*``(61681)
122, ``(61)*_c105_1*``(2305843009213693951)*``(768614336404564651)
124, ``(31)*``(67)*_c95_1*``(14066893)*``(715827883)*``(2147483647)*``(74747)*``(384773)*``(49477)*``(8681)*``(5581)
126, ``(3)^2*``(7)*``(73)*``(103)*``(337)*``(409)*_c125_1*``(649657)*``(5419)*``(92737)
128, ``(257)*``(641)*_c133_1*``(65537)*``(35089)*``(274177)
130, ``(5)*``(13)*``(31)*``(149)*``(463)*_c122_2*``(409891)*``(2264267)*``(7623851)*``(8191)*``(2731)
132, ``(3)*``(11)*``(89)*``(397)*``(683)*_c119_1*``(804889)*``(4327489)*``(599479)*``(312709)*``(20857)*``(2113)
134, ``(67)*_c149_1*``(42859)*``(7327657)
136, ``(17)^3*``(953)*_c140_1*``(131071)*``(43691)*``(354689)*``(26317)
138, ``(3)*``(23)*_c148_1*``(9733)*``(2957)*``(2796203)*``(178481)
140, ``(5)*``(7)*``(31)*``(37)*``(41)*``(43)*``(113)*``(127)*``(281)*_c123_1*``(47392381)*``(86171)*``(6251263)*``(122921)*``(7416361)*``(17681)
142, ``(71)*_c165_1*``(228479)*``(4003)
144, ``(3)^2*``(97)*``(109)*``(241)*``(257)*``(433)*``(577)*``(673)*_c157_1*``(38737)
146, ``(73)*``(439)*_c168_1*``(2298041)*``(1753)
148, ``(37)*``(223)*``(593)*_c146_1*``(616318177)*``(172331)*``(231769777)*``(30817)*``(1979)*``(1777)
150, ``(3)*``(5)^2*``(251)*``(331)*``(601)*_c156_1*``(153427)*``(10567201)*``(100801)*``(4051)*``(1801)
152, ``(17)*``(19)*``(131)*``(229)*``(457)*``(1217)*_c151_1*``(9743)*``(230165249)*``(174763)*``(524287)*``(148961)
154, ``(7)*``(11)*``(43)*``(89)*``(127)*``(617)*``(683)*_c153_1*``(35532364099)*``(1569473)*``(78233)*``(2213)*``(125929)
156, ``(3)*``(13)*``(293)*``(313)*``(953)*``(1249)*``(1613)*_c163_1*``(121369)*``(8191)*``(2731)*``(3121)*``(21841)
158, ``(79)*_c180_1*``(10463)*``(50929)*``(5309)*``(42487)*``(2687)
160, ``(5)*``(31)*``(59)*``(257)*_c190_1*``(65537)*``(61681)
162, ``(3)^4*``(73)*``(881)*_c173_1*``(1356077)*``(71119)*``(87211)*``(135433)*``(262657)*``(2593)
164, ``(41)*``(257)*_c193_1*``(43249589)*``(13367)*``(10169)
166, ``(83)*``(499)*``(971)*``(1163)*_c197_1*``(155377)*``(2657)
168, ``(3)*``(7)*``(17)*``(101)*``(113)*``(127)*``(241)*``(337)*``(1429)*_c180_2*``(15790321)*``(5419)*``(14449)*``(28211)*``(3361)
170, ``(5)*``(17)*``(31)*_c210_1*``(131071)*``(43691)
172, ``(43)*``(431)*``(1613)*_c205_1*``(500177)*``(101653)*``(9719)
174, ``(3)*``(29)*``(233)*``(379)*``(617)*``(1103)*_c207_1*``(8419)*``(2089)*``(4177)
176, ``(11)*``(37)*``(257)*``(353)*``(397)*``(683)*``(1301)*_c201_1*``(119782433)*``(229153)*``(2113)
178, ``(89)*_c224_1*``(9433)*``(62020897)
180, ``(3)^2*``(5)*``(41)*``(73)*``(109)*``(151)*``(331)*``(631)*``(1321)*_c194_1*``(29247661)*``(403783)*``(23311)*``(18837001)*``(54001)
182, ``(7)*``(13)*``(43)*``(127)*``(911)*_c199_1*``(23140471537)*``(1210483)*``(112901153)*``(8191)*``(2731)*``(224771)
184, ``(17)*``(23)*``(277)*``(1013)*``(1657)*_c215_1*``(2796203)*``(178481)*``(30269)*``(389621)
186, ``(3)*``(31)*``(353)*_c210_2*``(2903110321)*``(1301919607)*``(715827883)*``(2147483647)
188, ``(47)*``(283)*_c228_1*``(13264529)*``(53377)*``(2351)*``(3761)*``(4513)
190, ``(5)*``(19)*``(31)*``(67)*_c235_1*``(174763)*``(524287)*``(2281)*``(5101)
192, ``(3)*``(241)*``(257)*``(641)*``(673)*_c246_1*``(65537)
194, ``(97)*``(467)*``(971)*``(1553)*_c246_2*``(11447)*``(31817)
196, ``(7)^2*``(43)*``(113)*``(127)*``(461)*_c259_1
198, ``(3)^2*``(11)*``(73)*``(89)*``(683)*_c238_1*``(34470847)*``(599479)*``(153649)*``(20857)*``(5347)
200, ``(5)^2*``(17)*``(31)*``(251)*``(389)*``(401)*``(601)*``(691)*_c226_1*``(61681)*``(268501)*``(2787601)*``(340801)*``(8101)*``(4051)*``(1801)
202, ``(101)*``(1297)*_c270_1*``(145121)
204, ``(3)*``(17)*``(137)*``(307)*``(409)*``(953)*_c235_2*``(131071)*``(43691)*``(11119)*``(13669)*``(26317)*``(2143)*``(2857)*``(6529)*``(3061)
206, ``(103)*``(1291)*_c270_2*``(22643)*``(46654213)
208, ``(13)*``(157)*``(257)*``(1613)*_c269_1*``(8191)*``(2731)*``(858001)
210, ``(3)*``(5)*``(7)*``(127)*``(151)*``(281)*``(331)*``(337)*_c240_1*``(86171)*``(122921)*``(152041)*``(29191)*``(106681)*``(664441)*``(5419)*``(1564921)
212, ``(37)*``(53)*_c264_1*``(1801439824104653)*``(69431)*``(20394401)*``(6361)
214, ``(107)*``(643)*_c294_1*``(4339)
216, ``(3)^3*``(17)*``(241)*``(433)*_c253_1*``(29567)*``(38737)*``(33975937)*``(4663)*``(87211)*``(279073)*``(262657)*``(3851)*``(246241)
218, ``(59)*``(109)*``(157)*_c287_1*``(104124649)*``(6379)*``(13721)
220, ``(5)*``(11)*``(31)*``(41)*``(89)*``(397)*``(683)*``(797)*``(881)*``(1297)*_c271_1*``(171253)*``(3191)*``(201961)*``(2971)*``(2113)
222, ``(3)*``(37)*``(557)*_c279_1*``(616318177)*``(26295457)*``(17539)*``(321679)*``(3331)*``(1777)
224, ``(7)*``(43)*``(127)*``(257)*``(449)*``(659)*``(1483)*_c273_1*``(65537)*``(13259)*``(183076097)*``(15790321)*``(5153)*``(2689)
226, ``(113)*``(631)*_c279_2*``(636190001)*``(23279)*``(65993)*``(1868569)*``(3391)*``(48817)*``(40194577)
228, ``(3)*``(19)*``(103)^2*``(457)*``(571)*_c291_1*``(160969)*``(174763)*``(524287)*``(32377)*``(131101)
230, ``(5)*``(23)*``(31)*``(691)*_c289_1*``(4036961)*``(2796203)*``(178481)*``(1884103651)*``(44371)*``(14951)
232, ``(17)*``(29)*``(1103)*_c322_1*``(59393)*``(2089)
234, ``(3)^2*``(13)*``(73)*``(937)*``(1367)*_c308_1*``(121369)*``(86113)*``(8191)*``(6553)*``(2731)
236, ``(59)*``(647)*``(1181)*_c297_1*``(5521693)*``(157649)*``(6521)*``(179951)*``(174877)*``(37171)*``(3541)*``(2833)
238, ``(7)*``(17)*``(43)*``(127)*_c323_1*``(131071)*``(43691)*``(14767)*``(20231)
240, ``(3)*``(5)*``(97)*``(151)*``(257)*``(331)*``(421)*``(673)*``(1321)*_c309_1*``(249107671)*``(4562284561)*``(61681)
242, ``(11)^2*``(89)*``(647)*``(683)*``(727)*_c320_1*``(2159191)*``(117371)*``(2371)*``(1889)*``(2927)
244, ``(61)*``(733)*_c307_1*``(2305843009213693951)*``(768614336404564651)*``(3456749)*``(1709)
246, ``(3)*``(41)*``(739)*_c337_1*``(3887047)*``(13367)*``(19553)*``(165313)
248, ``(17)*``(31)*``(37)*_c314_1*``(715827883)*``(2147483647)*``(290657)*``(564097)*``(384773)*``(49477)*``(8681)*``(5581)
250, ``(5)^3*``(31)*``(601)*_c356_1*``(4051)*``(1801)
252, ``(3)^2*``(7)*``(73)*``(109)*``(113)*``(337)*``(1429)*_c337_2*``(649657)*``(4783)*``(5419)*``(14449)*``(92737)
254, ``(127)*_c375_1
256, ``(67)*``(641)*_c366_1*``(65537)*``(274177)
258, ``(3)*``(43)*``(431)*``(1033)*_c364_1*``(1591582393)*``(9719)
260, ``(5)*``(13)*``(31)*``(41)*``(157)*``(521)*``(761)*``(1613)*_c340_1*``(34110701)*``(409891)*``(7623851)*``(51481)*``(8191)*``(2731)
262, ``(131)*``(1049)*``(1193)*_c377_1*``(4744297)
264, ``(3)*``(11)*``(17)*``(241)*``(353)*``(397)*``(683)*_c338_1*``(4327489)*``(98618273953)*``(599479)*``(312709)*``(20857)*``(74201)*``(7393)*``(2113)
266, ``(7)*``(19)*``(43)*``(127)*``(157)*``(1381)*_c362_1*``(53717)*``(174763)*``(524287)*``(80349811)*``(4523)
268, ``(67)*``(101)*_c378_1*``(42875177)*``(15152453)*``(7327657)
270, ``(3)^3*``(5)*``(73)*``(151)*``(331)*``(547)*``(631)*``(811)*``(1663)*_c356_2*``(348031)*``(23311)*``(18837001)*``(87211)*``(262657)*``(15121)
272, ``(17)*``(257)*``(953)*_c380_1*``(131071)*``(43691)*``(354689)*``(383521)*``(26317)
274, ``(137)*``(1097)*_c406_1*``(15619)
276, ``(3)*``(23)*``(59)*``(1013)*``(1657)*_c389_1*``(2796203)*``(38971)*``(178481)*``(30269)
278, ``(139)*``(149)*_c388_1*``(450479)*``(707633)*``(5625767248687)*``(4506937)
280, ``(5)*``(7)*``(17)*``(31)*``(43)*``(113)*``(127)*``(347)*_c378_2*``(47392381)*``(86171)*``(122921)*``(15790321)*``(61681)*``(7416361)
282, ``(3)*``(47)*``(131)*_c391_1*``(62189)*``(1681003)*``(35273039401)*``(13264529)*``(2351)*``(4513)
284, ``(37)^2*``(71)*``(569)*_c402_1*``(228479)*``(148587949)*``(472287102421)
286, ``(11)*``(13)*``(89)*``(683)*_c389_2*``(16865476527940273)*``(6156182033)*``(724153)*``(2003)*``(8191)*``(2731)
288, ``(3)^2*``(109)*``(193)*``(241)*``(257)*``(433)*``(577)*``(673)*``(1153)*_c386_1*``(65537)*``(278452876033)*``(38737)*``(38941695937)*``(6337)
290, ``(5)*``(29)*``(31)*``(233)*``(751)*``(1103)*_c405_1*``(7109)*``(967289)*``(1778099)*``(2423)*``(7553921)*``(2089)
292, ``(73)*``(311)*``(439)*``(491)*_c427_1*``(2298041)*``(9929)*``(1753)
294, ``(3)*``(7)^2*``(127)*``(337)*_c438_1*``(748819)*``(5419)
296, ``(17)*``(37)*``(223)*``(593)*_c430_1*``(616318177)*``(231769777)*``(1777)
298, ``(149)*``(1193)*_c439_1*``(38369587)*``(650833)*``(26113)
300, ``(3)*``(5)^2*``(41)*``(251)*``(331)*``(353)*``(601)*``(1201)*``(1321)*_c407_1*``(268501)*``(2967583)*``(63901)*``(10567201)*``(100801)*``(8101)*``(4051)*``(1801)
302, ``(151)*``(283)*_c432_1*``(18717738334417)*``(2332951)*``(165799)*``(55871)*``(18121)
304, ``(19)*``(229)*``(257)*``(457)*``(1217)*``(1319)*_c439_2*``(174763)*``(524287)*``(148961)*``(27361)
306, ``(3)^2*``(17)*``(73)*``(919)*_c426_1*``(27983)*``(54787)*``(11359393)*``(131071)*``(43691)*``(11119)*``(2143)*``(2857)*``(123931)*``(6529)
308, ``(7)*``(11)*``(43)*``(89)*``(113)*``(127)*``(397)*``(617)*``(683)*_c434_1*``(35532364099)*``(12613)*``(78233)*``(5227)*``(8317)*``(2113)
310, ``(5)*``(31)^3*_c450_1*``(715827883)*``(2147483647)*``(73471)*``(11471)*``(11161)
312, ``(3)*``(13)*``(17)*``(241)*``(1249)*``(1613)*_c453_1*``(121369)*``(8191)*``(2731)*``(3121)*``(21841)*``(858001)
314, ``(157)*_c482_1*``(2350291)*``(15073)
316, ``(79)*``(233)*_c486_1*``(27617)*``(2687)
318, ``(3)*``(53)*_c469_1*``(13960201)*``(69431)*``(20394401)*``(6043)*``(6679)*``(6361)
320, ``(5)*``(31)*``(37)*``(257)*``(641)*_c469_2*``(65537)*``(120430291)*``(3602561)*``(23131)*``(61681)
322, ``(7)*``(23)*``(43)*``(67)*``(127)*``(1289)*_c488_1*``(2796203)*``(178481)
324, ``(3)^4*``(73)*_c466_1*``(71119)*``(3618757)*``(7309)*``(87211)*``(279073)*``(135433)*``(262657)*``(246241)*``(2593)
326, ``(163)*_c505_1*``(150287)*``(704161)
328, ``(17)*``(41)*_c500_1*``(43249589)*``(13367)*``(10169)*``(13121)
330, ``(3)*``(5)*``(11)*``(89)*``(103)*``(151)*``(683)*``(809)*``(881)*_c480_1*``(9138229)*``(599479)*``(20857)*``(3191)*``(201961)*``(2971)
332, ``(83)*``(499)*``(997)*``(1163)*_c501_1*``(13063537)*``(2939)*``(155377)*``(2657)
334, ``(59)*``(167)*_c524_1*``(2349023)
336, ``(3)*``(7)*``(97)*``(127)*``(241)*``(257)*``(491)*``(673)*``(1429)*_c494_1*``(15790321)*``(5419)*``(14449)*``(5153)*``(3361)*``(2017)
338, ``(13)^2*``(491)*``(617)*_c524_2*``(4057)*``(8191)*``(2731)
340, ``(5)*``(17)*``(31)*``(41)*``(137)*``(953)*``(1021)*_c499_1*``(23650061)*``(11489)*``(131071)*``(43691)*``(26317)*``(4421)*``(550801)
342, ``(3)^2*``(19)*``(73)*``(571)*_c517_1*``(5939)*``(93507247)*``(174763)*``(524287)*``(32377)
344, ``(17)*``(43)*``(431)*_c531_1*``(500177)*``(3559)*``(101653)*``(9719)
346, ``(173)*_c537_1*``(1505447)*``(730753)*``(4153)*``(6491)
348, ``(3)*``(29)*``(233)*``(1103)*``(1129)*_c534_1*``(5689)*``(7321)*``(29581)*``(2089)*``(4177)
350, ``(5)^2*``(7)*``(31)*``(43)*``(127)*``(251)*``(281)*``(601)*``(1051)*_c510_1*``(32009)*``(86171)*``(122921)*``(60816001)*``(39551)*``(110251)*``(4051)*``(1801)
352, ``(11)*``(257)*``(397)*``(683)*_c531_2*``(65537)*``(119782433)*``(5304641)*``(229153)*``(2861)*``(2113)
354, ``(3)*``(59)*``(271)*_c548_1*``(179951)*``(13099)*``(184081)*``(37171)*``(2833)
356, ``(37)*``(89)*``(1069)*_c565_1*``(62020897)
358, ``(179)*``(1409)*``(1433)*_c564_1*``(58745093521)
360, ``(3)^2*``(5)*``(17)*``(109)*``(151)*``(241)*``(331)*``(433)*``(631)*``(1321)*_c510_2*``(168692292721)*``(29247661)*``(3593)*``(38737)*``(4562284561)*``(61681)*``(23311)*``(18837001)*``(54001)
362, ``(181)*``(263)*_c566_1*``(7648337)*``(1164193)*``(43441)*``(1811)
364, ``(7)*``(13)*``(43)*``(113)*``(127)*``(157)*``(911)*``(1093)^2*``(1613)*_c533_1*``(23140471537)*``(1210483)*``(112901153)*``(4733)*``(8191)*``(2731)*``(224771)
366, ``(3)*``(61)*``(433)*_c546_1*``(89071)*``(2305843009213693951)*``(768614336404564651)*``(55633)*``(2441)
368, ``(23)*``(101)*``(257)*``(277)*``(1013)*``(1657)*_c570_1*``(2796203)*``(178481)*``(30269)*``(7681)
370, ``(5)*``(31)*``(37)*``(223)*``(1481)*_c580_1*``(616318177)*``(28136651)*``(1777)
372, ``(3)*``(31)*_c559_1*``(2903110321)*``(715827883)*``(2147483647)*``(2675483)*``(384773)*``(49477)*``(8681)*``(5581)
374, ``(11)*``(17)*``(89)*``(157)*``(683)*_c592_1*``(707983)*``(131071)*``(43691)
376, ``(17)*``(47)*``(283)*_c575_1*``(23592342593)*``(1198107457)*``(13264529)*``(2087)*``(2351)*``(3761)*``(4513)
378, ``(3)^3*``(7)*``(73)*``(337)*``(727)*_c580_2*``(649657)*``(431219)*``(119827)*``(5419)*``(92737)*``(87211)*``(262657)
380, ``(5)*``(19)*``(31)*``(41)*``(229)*``(457)*``(761)*_c597_1*``(174763)*``(524287)*``(54721)*``(2281)
382, ``(191)*``(401)*``(1307)*_c615_1*``(7068569257)
384, ``(3)*``(241)*``(257)*``(641)*``(673)*``(769)*_c613_1*``(65537)*``(274177)
386, ``(193)*_c628_1*``(13821503)*``(6563)
388, ``(67)*``(97)*``(971)*``(1553)*``(1669)*_c598_1*``(11447)*``(31817)*``(3555339061)*``(3881)*``(5821)*``(194569)*``(4657)
390, ``(3)*``(5)*``(13)*``(151)*``(331)*_c609_1*``(38639)*``(409891)*``(121369)*``(7623851)*``(107251)*``(8191)*``(2731)
392, ``(7)^2*``(17)*``(37)*``(43)*``(59)*``(113)*``(127)*_c611_1*``(375327457)*``(15790321)*``(1007441)*``(273617)*``(7057)
394, ``(197)*``(307)*_c650_1*``(7487)
396, ``(3)^2*``(11)*``(73)*``(89)*``(109)*``(683)*_c607_1*``(4327489)*``(599479)*``(312709)*``(153649)*``(20857)*``(42373)*``(235621)*``(5347)*``(2113)
398, ``(199)*_c659_1*``(664679)
400, ``(5)^2*``(31)*``(251)*``(257)*``(523)*``(601)*``(1601)*_c614_1*``(2909)*``(61681)*``(268501)*``(2787601)*``(340801)*``(8101)*``(4051)*``(1801)*``(25601)
402, ``(3)*``(67)*``(1609)*_c651_1*``(7327657)*``(22111)*``(2011)*``(9649)
404, ``(101)*``(809)*_c660_1*``(35608471)*``(2671)*``(3851)
406, ``(7)*``(29)*``(43)*``(127)*``(233)*``(1103)*_c664_1*``(136417)*``(2089)
408, ``(3)*``(17)^3*``(241)*``(307)*``(673)*``(953)*_c627_1*``(131071)*``(43691)*``(354689)*``(11119)*``(13669)*``(26317)*``(2143)*``(2857)*``(8161)*``(6529)*``(3061)
410, ``(5)*``(31)*``(41)*_c678_1*``(2940521)*``(13367)
412, ``(103)*``(131)*_c680_1*``(17325013)*``(41201)
414, ``(3)^2*``(23)*``(73)*_c680_2*``(2796203)*``(79903)*``(178481)
416, ``(13)*``(157)*``(257)*``(1613)*_c657_1*``(65537)*``(23877647873)*``(21193)*``(928513)*``(8191)*``(2731)*``(858001)
418, ``(11)*``(19)*``(89)*``(683)*``(887)*_c688_1*``(174763)*``(524287)
420, ``(3)*``(5)*``(7)*``(41)*``(113)*``(127)*``(151)*``(257)*``(281)*``(331)*``(337)*``(1321)*``(1429)*_c628_2*``(47392381)*``(86171)*``(122921)*``(152041)*``(29191)*``(106681)*``(7416361)*``(664441)*``(5419)*``(14449)*``(1564921)
Warning, computation interrupted
>