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A090943
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Even numbers n such that N(n) is divisible by a nontrivial square, m^2, say and GCD(n,m)=1, where N(n) is the numerator of the Bernoulli number B(n). The numbers m are given in A094095.
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3
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228, 284, 914, 1434, 1616, 2948, 3292, 4280, 4336, 5612, 5768, 6302, 6944, 7714, 7758, 8276, 9608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence consists of the union of an infinite number of arithmetic progressions. Let p be an irregular prime and let {m1,m2,...} be even numbers < p(p-1) such that p^2 | N(mi). Then each (p,mi) is a second-order irregular pair. This leads to the arithmetic progression n=mi+p(p-1)k for each i and for k=0,1,2,3... If we restrict the sequence to those pairs with mi < 10000, we find that only the pairs (37,284), (59,914), (67,3292), (101,5768), (103,228), (157,6302) and (271,1434) contribute terms to this sequence.
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LINKS
| Bernd Kellner, Ueber irregulaere Paare hoeherer Ordnungen [On irregular pairs of higher order], Diplomarbeit, Goettingen 2002.
S. S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers
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MATHEMATICA
| nn=10; s = Union[284 + 36*37*Range[0, nn], 914+58*59*Range[0, nn], 3292+66*67*Range[0, nn], 5768+100*101*Range[0, nn], 228+102*103*Range[0, nn], 6302+156*157*Range[0, nn], 1434+270*271*Range[0, nn]]; Select[s, #<=10000&]
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CROSSREFS
| Cf. A092681.
Sequence in context: A122976 A098245 A190027 * A154519 A128808 A043411
Adjacent sequences: A090940 A090941 A090942 * A090944 A090945 A090946
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KEYWORD
| nonn,nice
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Feb 27 2004
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