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A189684 Number of irregular pairs (p,2n). 3
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, 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, 7, 6, 3, 2, 6, 6, 6, 5, 6, 5, 7, 5, 4, 7, 8, 5, 3, 2, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

a(n) is the number of primes p >= 2n+3 that divide the numerator of the Bernoulli number B_{2n}.

LINKS

Table of n, a(n) for n=1..87.

B. Mazur, How can we construct abelian Galois extensions of basic number fields?, Bull. Amer. Math. Soc., 48 (2011), 155-209. See footnote 64 on p. 205.

Samual S. Wagstaff, Jr., Prime divisors of the Bernoulli and Euler numbers

Wikipedia, Irregular pairs

MATHEMATICA

Table[p = Select[First /@ FactorInteger[Abs[Numerator[BernoulliB[2n]]]], # >= 2*n+3 &]; Length[p], {n, 35}] (* T. D. Noe, Apr 25 2011 *)

CROSSREFS

Cf. A000367, A000928, A035112, A046753, A189683, A189685.

Sequence in context: A008334 A116858 A182134 * A308176 A106493 A083338

Adjacent sequences:  A189681 A189682 A189683 * A189685 A189686 A189687

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Apr 25 2011

STATUS

approved

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Last modified August 20 20:50 EDT 2019. Contains 326155 sequences. (Running on oeis4.)