A074181 Smallest power of n >= n!.

1, 2, 9, 64, 125, 1296, 16807, 262144, 531441, 10000000, 214358881, 5159780352, 10604499373, 289254654976, 8649755859375, 281474976710656, 582622237229761, 20822964865671168, 799006685782884121

Offset

1,2

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..447

Formula

From Danny Rorabaugh, Apr 14 2015: (Start)

a(n) = n^A074184(n).

a(n) = n^ceiling(log_n(n!)) for n>1.

a(n) = n*A074182(n) = n^A060151(n) = n^(1 + A039960(n)) = n! + A111683(n) for n>2.

(End)

Mathematica

Join[{1}, Table[n^Ceiling[Log[n, n!]], {n, 2, 20}]] (* Harvey P. Dale, Aug 10 2022 *)

Prog

(Sage) [1]+[n^ceil(log(factorial(n))/log(n)) for n in range(2, 20)] # Danny Rorabaugh, Apr 14 2015
(PARI) a(n)=if(n>2, n^(logint(n!, n)+1), n) \\ Charles R Greathouse IV, Oct 11 2015

Crossrefs

Cf. A074182.

Sequence in context: A253109 A167913 A076944 * A052513 A216839 A024720

Adjacent sequences: A074178 A074179 A074180 * A074182 A074183 A074184

Keyword

nonn,easy

Author

Amarnath Murthy, Aug 31 2002

Extensions

More terms from Jason Earls, Sep 02 2002

Status

approved