

A111683


n^k  n! where n^k > n! >= n^(k1).


4



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



