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Numbers m such that the numerator of the Bernoulli number B(m) is divisible by p^4, where p is prime.
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%I #31 May 13 2020 08:53:12

%S 1250,3750,4802,6250,8750,9604

%N Numbers m such that the numerator of the Bernoulli number B(m) is divisible by p^4, where p is prime.

%C For each m in the current sequence, the smallest prime p such that p^4 divides the numerator of the Bernoulli number B(m) is listed in A122273.

%C Note that the numerator of B(6250) is divisible by 5^5.

%C The current sequence is a subsequence of A122270, which are the numbers m such that the numerator of the Bernoulli number B(m) is divisible by a cube.

%C Sequence A122270 itself is a subsequence of A090997, which are the numbers m such that the numerator of the Bernoulli number B(m) is divisible by a square. [Edited by _Petros Hadjicostas_, May 12 2020]

%H The Bernoulli Number Page, <a href="https://www.bernoulli.org/download/bn_factors.txt">Table of factors of the numerators of Bernoulli numbers Bn in the range n = 2..10000</a>, 2018.

%H S. S. Wagstaff, Jr, <a href="http://www.cerias.purdue.edu/homes/ssw/bernoulli/bnum">Prime factors of the absolute values of Bernoulli numerators</a>, 2018.

%e a(1) = 1250 because 5^4 divides numerator(B(1250)).

%e a(3) = 4802 because 7^4 divides numerator(B(4802)).

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

%K nonn,more

%O 1,1

%A _Alexander Adamchuk_, Aug 28 2006