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

1,2

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

Links

Table of n, a(n) for n=1..25.

Example

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

Mathematica

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

Crossrefs

Cf. A036679, A109663.

Sequence in context: A358829 A225792 A057293 * A116222 A338234 A048038

Adjacent sequences: A109659 A109660 A109661 * A109663 A109664 A109665

Keyword

base,more,nonn

Author

Ryan Propper, Aug 06 2005

Extensions

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

Status

approved