A111683 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A153745 A076724 A080393 * A323734 A347817 A088984

Adjacent sequences: A111680 A111681 A111682 * A111684 A111685 A111686

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Aug 16 2005

EXTENSIONS

More terms from Stefan Steinerberger, Jan 26 2006

STATUS

approved