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a(n) is the smallest prime whose cube divides the numerator of the Bernoulli number B(A122270(n)).
5

%I #28 Sep 15 2024 20:23:49

%S 5,7,5,5,7,5,5,11,7,5,5,7,5,5,13,5,7,5,7,5,5,5,7,5,7,5,11,5,5,13,7,5,

%T 7,5,17

%N a(n) is the smallest prime whose cube divides the numerator of the Bernoulli number B(A122270(n)).

%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) = 5 because 5^3 divides numerator(B(A122270(1))) = numerator(B(250)), but 3^3 does not.

%Y Cf. A000367, A090997, A090987, A122270, A122272, A122273.

%K nonn,more

%O 1,1

%A _Alexander Adamchuk_, Aug 28 2006

%E Various sections edited by _Petros Hadjicostas_, May 12 2020