A074182 Largest power of n <= n!.

1, 2, 3, 16, 25, 216, 2401, 32768, 59049, 1000000, 19487171, 429981696, 815730721, 20661046784, 576650390625, 17592186044416, 34271896307633, 1156831381426176, 42052983462257059, 1638400000000000000

Offset: 1

Author

Amarnath Murthy, Aug 31 2002

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A039960, A060151, A074181.

Programs

Magma

[1] cat [n^Floor(Log(Factorial(n)) / Log(n)): n in [2..25]]; // Vincenzo Librandi, Apr 15 2015

PARI

a(n)=if(n>3,n^logint(n!,n),n) \\ Charles R Greathouse IV, Oct 11 2015

Sage

[1] + [n^(floor(log(factorial(n))/log(n))) for n in range(2, 21)] # Danny Rorabaugh, Apr 14 2015

Formula

From Danny Rorabaugh, Apr 14 2015: (Start)

a(n) = n^A039960(n) = n^(A060151(n)-1).

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

a(n) = A074181(n)/n for n>2.

(End)

Extensions

More terms from Jason Earls, Sep 02 2002