A109662 Numbers k such that the sum of the digits of (k^k - k!) is divisible by k.

1, 2, 3, 9, 14, 15, 29, 33, 45, 81, 102, 105, 126, 142, 157, 288, 414, 1184, 2133, 10449, 16369, 17221, 46524, 214179, 216741

Offset: 1

Author

Ryan Propper, Aug 06 2005

Keywords

• base
• more
• nonn

Comments

The quotients are 0, 1, 1, 5, 5, 6, 7, 6, 8, 9, 9, 9, 9, 10, 10, 11, 12, 14, 15, 18, 19, 19, 21, 24, 24.

No more terms < 500000. - Lars Blomberg, Jul 05 2011

a(26) > 595261. - J.W.L. (Jan) Eerland, Nov 05 2024

Examples

			The digits of 414^414 - 414! sum to 4968 and 4968 is divisible by 414, so 414 is in the sequence.
		

Crossrefs

Cf. A036679, A109663.

Programs

Mathematica

Do[s = n^n - n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]

Extensions

Terms a(20)-a(25) from Lars Blomberg, Jul 05 2011