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%I #25 Mar 17 2023 05:52:03
%S 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,
%T 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,
%U 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
%N a(n) is the smallest prime whose square divides the numerator of the Bernoulli number B(A090997(n)).
%C 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
%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.
%Y Cf. A000367, A090997, A094095, A122270, A122271, A122272, A122273.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Feb 28 2004
%E 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
%E More terms from _Alexander Adamchuk_, Aug 19 2006
%E Various sections edited by _Petros Hadjicostas_, May 12 2020
%E Corrected and terms a(33) onward added by _Max Alekseyev_, Mar 16 2023
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