A100685 - OEIS

%I #21 Nov 21 2021 05:05:50

%S 1,2,4,6,8,16,24,32,36,64,120,128,216,256,512,576,720,1024,1296,2048,

%T 4096,5040,7776,8192,13824,14400,16384,32768,40320,46656,65536,131072,

%U 262144,279936,331776,362880,518400,524288,1048576,1679616,1728000

%N Powers of factorials A000142.

%C Subsequence of A001013. Supersequence of A036740 without its first term.

%C Supersequence also of A046882 and A055209 without their first terms. - _Jonathan Sondow_ and _Robert G. Wilson v_, Dec 19 2004

%H G. C. Greubel, <a href="/A100685/b100685.txt">Table of n, a(n) for n = 1..9660</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers.</a>

%F Sum_{n>=1} 1/a(n) = 1 + A331373. - _Amiram Eldar_, Nov 21 2021

%e 24 = (4!)^1 and 36 = (3!)^2.

%t With[{ln = Log[10!]}, Table[With[{f = m!}, Table[f^j, {j, 0, Floor[ln/Log[f]]}]], {m, 2, 10}]] //Flatten //Union

%Y Cf. A000142, A001013, A036740, A331373.

%Y Cf. also A046882 and A055209.

%Y Subsequences: A000079, A000400, A009968.

%K easy,nonn

%O 1,2

%A Kyle Schalm and _Jonathan Sondow_, Dec 08 2004