A100685 Powers of factorials A000142.

1, 2, 4, 6, 8, 16, 24, 32, 36, 64, 120, 128, 216, 256, 512, 576, 720, 1024, 1296, 2048, 4096, 5040, 7776, 8192, 13824, 14400, 16384, 32768, 40320, 46656, 65536, 131072, 262144, 279936, 331776, 362880, 518400, 524288, 1048576, 1679616, 1728000

Offset: 1

Author

Kyle Schalm and Jonathan Sondow, Dec 08 2004

Keywords

• easy
• nonn

Comments

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

Supersequence also of A046882 and A055209 without their first terms. - Jonathan Sondow and Robert G. Wilson v, Dec 19 2004

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..9660
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000142, A001013, A036740, A331373.

Cf. also A046882 and A055209.

Subsequences: A000079, A000400, A009968.

Programs

Mathematica

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

Formula

Sum_{n>=1} 1/a(n) = 1 + A331373. - Amiram Eldar, Nov 21 2021