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

1,2

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..9660

Index entries for sequences related to factorial numbers.

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000142, A001013, A036740, A331373.

Cf. also A046882 and A055209.

Subsequences: A000079, A000400, A009968.

Sequence in context: A379169 A064408 A316225 * A296993 A068799 A317306

Adjacent sequences: A100682 A100683 A100684 * A100686 A100687 A100688

Keyword

easy,nonn

Author

Kyle Schalm and Jonathan Sondow, Dec 08 2004

Status

approved