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

Author

Amarnath Murthy, Aug 31 2002

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A074182.

Programs

Mathematica

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

PARI

a(n)=if(n>2,n^(logint(n!,n)+1),n) \\ Charles R Greathouse IV, Oct 11 2015

Sage

[1]+[n^ceil(log(factorial(n))/log(n)) for n in range(2,20)] # Danny Rorabaugh, Apr 14 2015

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)

Extensions

More terms from Jason Earls, Sep 02 2002