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%I #5 Mar 27 2021 23:51:13
%S 1,1,2,2,3,7,6,6,6,8,11,9,29,14,23,20,19,14,33,22,61,19,35,47,79,22,
%T 38,26,49,27,34,27,34,30,55,29,46,40,32,32,46,35,40,46,38,52,46,85,
%U 203,41,48,44,48,73,58,50,55,71,48,103,49,139,71,58,74,151,77
%N Value of s in best integer approximation r^s to n! with s >= r.
%C The best approximation can be smaller or larger than n!; that is, minimize abs(n!-r^s).
%C In the case of a tie, choose the smallest possible s (for example, when n=3, n!=6, we have 2^2 <= 6 <= 2^3 equally distant, choose 2^2).
%e a(4) = 3, since 3^3 - 3 = 24 = 4! (note 5^2-1 = 24 is not allowed because 2 < 5).
%e a(7) = 6, since 4^6 + 944 = 5040 = 7! and there is no closer approximation.
%Y Cf. A342847, A342849, A045772, A045773.
%K nonn
%O 0,3
%A _Sean A. Irvine_, Mar 26 2021
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