A187751 a(n) = n^(n!) mod (n!)^n.

0, 0, 0, 81, 225280, 7991790625, 1078848154238976, 65180706714634067542224001, 1650157594512930366268925848349310976, 66807065275536807794426016376688705273224158387201, 228020326859403543540241849077865865705999564800000000000000000000

Offset: 0

Author

Alex Ratushnyak, Jan 03 2013

Keywords

• nonn

Examples

			a(3) = 3^6 mod 6^3 = 729 mod 216 = 81.
		

Crossrefs

Cf. A053986, A036740.

Programs

Maxima

A187751(n):=mod(n^(n!),(n!)^n)$ makelist(A187751(n),n,0,9); /* Martin Ettl, Jan 13 2013 */

Python

import math
for n in range(12):
  f = math.factorial(n)
  print(pow(n, f, f**n))

Formula

a(n) = A053986(n) mod A036740(n).

Extensions

a(10) from David Radcliffe, Jul 05 2025