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%I #21 Oct 09 2019 20:56:53
%S 0,0,0,0,0,1,0,1,1,2,2,2,1,2,2,3,1,1,1,2,1,4,2,3,2,4,3,3,4,3,4,2,2,4,
%T 3,2,1,2,3,5,3,5,3,3,3,3,5,5,5,5,5,3,4,3,5,3,1,4,1,3,3,7,3,6,5,3,4,3,
%U 7,6,3,2,6,6,6,5,6,5,7,5,4,7,8,5,3,2,7
%N Number of irregular pairs (p,2n).
%C a(n) is the number of primes p >= 2n+3 that divide the numerator of the Bernoulli number B_{2n}.
%H B. Mazur, <a href="https://doi.org/10.1090/S0273-0979-2011-01326-X">How can we construct abelian Galois extensions of basic number fields?</a>, Bull. Amer. Math. Soc., 48 (2011), 155-209. See footnote 64 on p. 205.
%H Samual S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/bernoulli/full.pdf">Prime divisors of the Bernoulli and Euler numbers</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_prime#Irregular_pairs"> Irregular pairs</a>
%t Table[p = Select[First /@ FactorInteger[Abs[Numerator[BernoulliB[2n]]]], # >= 2*n+3 &]; Length[p], {n, 35}] (* _T. D. Noe_, Apr 25 2011 *)
%Y Cf. A000367, A000928, A035112, A046753, A189683, A189685.
%K nonn
%O 1,10
%A _Jonathan Sondow_, Apr 25 2011
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