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A376397 a(n) = A276075(n!), where A276075 is the factorial base log-function.

%I A376397 #8 Oct 28 2024 16:23:37
%S A376397 0,1,3,5,11,14,38,41,45,52,172,176,896,921,929,933,5973,5978,46298,
%T A376397 46306,46332,46453,409333,409338,409350,410071,410077,410103,4038903,
%U A376397 4038912,43955712,43955717,43955839,43960880,43960910,43960916,522962516,523002837,523003559,523003568,6750024368,6750024395,93928315595
%N A376397 a(n) = A276075(n!), where A276075 is the factorial base log-function.
%H A376397 Antti Karttunen, <a href="/A376397/b376397.txt">Table of n, a(n) for n = 1..3000</a>
%H A376397 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A376397 a(n) = A276075(A000142(n)).
%F A376397 a(n) = Sum_{i=1..n} A276075(i).
%o A376397 (PARI)
%o A376397 A276075(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*(primepi(f[k, 1])!)); };
%o A376397 A376397(n) = A276075(n!);
%Y A376397 Partial sums of A276075.
%Y A376397 Cf. A000142.
%Y A376397 Cf. also A007489, A336415, A376398.
%K A376397 nonn
%O A376397 1,3
%A A376397 _Antti Karttunen_, Oct 28 2024