1,1

The smallest prime p such that p^4 divides the Numerator of BernoulliB[ a(n) ] are given in A122273[n] = {5,5,7,5,5,7,...}. Note that numerator of BernoulliB[6250] is divisible by 5^5. a(n) is a subset of A122270[n] = {250,686,750,1250,1372,1750,...} Numbers n such that numerator of Bernoulli number B(n) is divisible by a cube. a(n) is also a subset of A090997[n] = {50,98,150,196,228,242,250,...} Numbers n such that numerator of Bernoulli number B(n) is divisible by a square.

Table of factors of the numerators of Bernoulli numbers Bn in the range n=2,...,10000. at www.bernoulli.org

A122273[n]^4 divides numerator of BernoulliB[ A122272(n) ].

a(1) = 1250 because 5^4 divides Numerator[ BernoulliB[ 1250 ] ].

a(3) = 4802 because 7^4 divides Numerator[ BernoulliB[ 4802 ] ].

Cf. A122273, A000367, A090997, A090987, A122270, A122271.

Sequence in context: A020384 A086709 A120376 this_sequence A106322 A035762 A107558

Adjacent sequences: A122269 A122270 A122271 this_sequence A122273 A122274 A122275

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 28 2006