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A090943 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. 3
228, 284, 914, 1434, 1616, 2948, 3292, 4280, 4336, 5612, 5768, 6302, 6944, 7714, 7758, 8276, 9608 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..17.

Bernd Kellner, Über 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


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&]


Cf. A092681.

Sequence in context: A122976 A098245 A190027 * A252451 A305063 A258550

Adjacent sequences:  A090940 A090941 A090942 * A090944 A090945 A090946




T. D. Noe, Feb 27 2004



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Last modified August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)