A111683 n^k - n! where n^k > n! >= n^(k-1).

2, 3, 40, 5, 576, 11767, 221824, 168561, 6371200, 174442081, 4680778752, 4377478573, 202076363776, 7342081491375, 260552186822656, 226934809133761, 14420591159943168, 677361585374052121, 30335097991823360000

Offset: 2

Author

Amarnath Murthy, Aug 16 2005

Keywords

• nonn
• easy

Examples

			a(5) = 125 - 120 = 5, because 125 > 120 >= 25.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 2..447

Programs

Mathematica

For[n = 2, n < 20, n++, k := 0; While[n^k <= n!, k++ ]; Print[n^k - n! ]] (* Stefan Steinerberger, Jan 26 2006 *)

Sage

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

Formula

a(n) = n^(1+floor(log_n(n!))) - n! = n^A060151(n) - A000142(n). - Danny Rorabaugh, Apr 14 2015

Extensions

More terms from Stefan Steinerberger, Jan 26 2006