A109663 Numbers k such that the sum of the digits of (k^k + k!) is divisible by k.

1, 2, 3, 9, 15, 18, 27, 36, 51, 81, 93, 169, 181, 348, 444, 504, 528, 1881, 2031, 9843, 16479, 16685, 45435, 129056, 138510, 214008, 358326

Offset

1,2

Comments

The quotients are 2, 3, 2, 6, 6, 5, 8, 7, 6, 9, 9, 10, 10, 12, 12, 12, 12, 15, 15, 18, 19, 19, 21, 23, 22, 24, 25.

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

Links

Table of n, a(n) for n=1..27.

Example

The digits of 1881^1881 + 1881! sum to 28215 and 28215 is divisible by 1881, so 1881 is in the sequence.

Mathematica

Do[s = n^n + n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]
Select[Range[360000], Divisible[Total[IntegerDigits[#^#+#!]], #]&] (* Harvey P. Dale, Dec 27 2018 *)

Crossrefs

Cf. A053042, A109662.

Sequence in context: A245594 A078610 A108825 * A056702 A294126 A091361

Adjacent sequences: A109660 A109661 A109662 * A109664 A109665 A109666

Keyword

base,more,nonn

Author

Ryan Propper, Aug 06 2005

Extensions

a(21)-a(27) from Lars Blomberg, Jul 05 2011

Status

approved