A202358 Sum of digits of n^(n!).

0, 1, 4, 18, 73, 334, 2592, 18919, 164476, 1558521, 1, 187044031, 2326111614, 31214008090

Offset: 0

Author

Jacques ALARDET, Dec 17 2011

Keywords

• nonn
• base
• more

Comments

a(10^k) = 1. - Chai Wah Wu, Dec 18 2019

Examples

			a(3) = 18 because 3^3! = 729 with digit sum 7+2+9 = 18.
		

Crossrefs

Cf. A053986, A007953, A202336.

Programs

Maple

ds:= proc(n) local r;
       `if`(n<10, n, ds(iquo(n, 10^iquo(length(n), 2), 'r'))+ds(r))
     end:
a:= n-> ds(n^n!):
seq(a(n), n=0..10);  # Alois P. Heinz, Dec 17 2011

Python

from math import factorial
def a(n): return sum(map(int, str(n**(factorial(n)))))
print([a(n) for n in range(10)]) # Michael S. Branicky, Jan 28 2021

Formula

a(n) = A007953(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

a(11)-a(12) from Lars Blomberg, Jan 18 2013

a(13) from Chai Wah Wu, Oct 25 2021