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%I #42 Nov 22 2023 22:10:59
%S 0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,
%T 6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,
%U 9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11
%N a(n) = floor(sqrt(log_10(n!))).
%C Every nonnegative integer occurs at least 4 times.
%C Each integer k > 14 appears fewer than k times.
%C The only integers k that occur exactly k times are 11, 13 and 14.
%F a(n) = floor(sqrt(A034886(n) - 1)).
%F a(n) = A000196(A034886(n) - 1).
%t Array[Floor@ Sqrt[Log10[#!]] &, 93, 0]
%o (PARI) a(n) = sqrtint(log(n!)/log(10)); \\ _Michel Marcus_, Sep 27 2023
%Y Cf. A000196, A034886.
%K nonn
%O 0,9
%A _Paul F. Marrero Romero_, Aug 17 2023