A090987 a(n) is the smallest prime whose square divides the numerator of the Bernoulli number B(A090997(n)).

5, 7, 5, 7, 103, 11, 5, 37, 13, 5, 7, 5, 11, 7, 5, 17, 5, 13, 7, 19, 11, 5, 7, 5, 59, 5, 11, 7, 13, 5, 23, 7, 5, 17, 37, 5, 7, 5, 13, 7, 271, 19, 5, 11, 5, 7, 37, 5, 7, 29, 13, 11, 17, 5, 5, 7, 31, 11, 5, 7, 5, 23, 5, 7, 19, 11, 5, 7, 17, 5, 13, 5, 103, 37, 7, 5, 59, 5, 11, 13, 37, 7, 5, 7, 5, 131, 19, 17, 11, 37, 5, 7, 13, 5, 7, 11, 5, 23, 5, 67, 7, 5, 41, 29, 13, 11, 7, 5, 17, 5, 19, 7, 5, 43, 13, 7, 5, 31, 37, 5, 11, 67, 7, 5, 7, 17, 5, 11, 5, 7, 23, 5, 37, 7, 19, 59, 5, 11, 13, 47, 5, 7, 5, 11, 7, 5, 13, 5, 7, 5, 7, 5

Offset: 1

Author

N. J. A. Sloane, Feb 28 2004

Keywords

• nonn

Comments

It appears that, except for irregular primes belonging to A094095, such as a(5) = 103, a(8) = 37 and a(26) = 59, all regular prime a(n) = p divide the corresponding numerators of the Bernoulli numbers B(A090997(n)) with indices of the form 2*k*p^2, where k > 0 is an integer. - Alexander Adamchuk, Aug 19 2006

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, A090997, A094095, A122270, A122271, A122272, A122273.

Extensions

In view of the phrase "it appears", it is not clear to me that the correctness of this sequence has been rigorously established. - N. J. A. Sloane, Aug 26 2006

More terms from Alexander Adamchuk, Aug 19 2006

Various sections edited by Petros Hadjicostas, May 12 2020

Corrected and terms a(33) onward added by Max Alekseyev, Mar 16 2023