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%I #10 May 30 2012 02:53:03
%S 1,2,4,7,11,17,22,29,36,43,51,60,68,76,86,96,105,116,125,136,149,159,
%T 170,183,193,206,219,230,241,254,268,281,293,306,322,335,347,362,377,
%U 390,403,417,433,447,464,475,493,508,521,537,551,568,585,598,614,632
%N Number of powers of factorials not exceeding n!.
%C a(n) is the position of n! in A100685 (powers of factorials). a(n) < A101976(n) for n > 3 and a(n) < A101977(n) for n > 10.
%H Donovan Johnson, <a href="/A101978/b101978.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers.</a>
%e a(4) = 7 because 7 powers of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 16 and 24.
%t p[n_] := If[n>1, Union[Flatten[With[{ln=Log[n! ]}, Table[With[{f=m!}, Table[f^j, {j, 0, Floor[ln/Log[f]]}]], {m, 2, n}]]]], {1}]; Table[Length[p[n]], {n, 100}]
%Y Cf. A000142, A100685, A101976, A101977.
%K nonn
%O 1,2
%A _Jonathan Sondow_, Dec 22 2004
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