A122272 Numbers m such that the numerator of the Bernoulli number B(m) is divisible by p^4, where p is prime.

1250, 3750, 4802, 6250, 8750, 9604

Offset: 1

Author

Alexander Adamchuk, Aug 28 2006

Keywords

• nonn
• more

Comments

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.

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

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.

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]

Examples

			a(1) = 1250 because 5^4 divides numerator(B(1250)).
a(3) = 4802 because 7^4 divides numerator(B(4802)).
		

Links

• The Bernoulli Number Page, Table of factors of the numerators of Bernoulli numbers Bn in the range n = 2..10000, 2018.
• S. S. Wagstaff, Jr, Prime factors of the absolute values of Bernoulli numerators, 2018.

Crossrefs

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