%I #19 Sep 08 2022 08:45:56
%S 1,1,1,-1,-1,-3617,-7709321041217,
%T -106783830147866529886385444979142647942017
%N Numerators of Bernoulli numbers B(2^n).
%C Interestingly, the terms |a(n)| mod 100 show some regularity : 1, 1, 1, 1, 1, 17, 17, 17, 17, 69, 69, 69, 69, 69, 69, 69, 69, 53, 53, 53, 53, 53, ...
%C The only prime term up to a(20) is a(5)
%F a(n) = A164555(A131577(n))
%t A164555[n_] := If[n <= 2, 1, BernoulliB[n] // Numerator]; A131577[n_] := If[n == 0, 0, 2^(n-1)]; a[n_] := A164555[A131577[n]];
%t (* or *) a[n_] := n!*Coefficient[ Series[x/(1-Exp[-x]), {x, 0, 2^6}], x, Max[1, 2^(n-1)]] // Numerator; Table[a[n], {n, 0, 7}]
%o (Magma)
%o A164555:=func<n | n le 2 select 1 else Numerator(Bernoulli(n))>;
%o [A164555(2^(n-1)): n in [0..10]]; // _Bruno Berselli_, Jan 09 2013
%K sign,frac
%O 0,6
%A _Jean-François Alcover_, Jan 03 2013