A109656 Numbers n such that the sum of the digits of sum_{k=1..n}(k^k) is divisible by n.

1, 13, 15, 22, 25, 107, 115, 149, 163, 472, 808, 1347, 1979, 27594, 77150

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

sum_{k=1..13}(k^k) = 312086923782437; the digits of 312086923782437 sum to 65, which is divisible by 13, so 13 is in the sequence.

Mathematica

s = 0; Do[s += n^n; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10^5}]
Module[{nn=2000, pwr}, pwr=Accumulate[Table[n^n, {n, nn}]]; Select[Thread[ {Range[nn], pwr}], Divisible[Total[IntegerDigits[#[[2]]]], #[[1]]]&]][[All, 1]] (* The program generates the first 13 terms of the sequence. To generate more, increase the nn constant, but the program may take a long time to run and the computer may run out of memory. *) (* Harvey P. Dale, Dec 19 2021 *)

Crossrefs

Sequence in context: A257492 A067912 A140646 * A367949 A178724 A087814

Adjacent sequences: A109653 A109654 A109655 * A109657 A109658 A109659

Keyword

nonn,base

Author

Ryan Propper, Aug 06 2005

Extensions

More terms from Ryan Propper, Nov 13 2005

Status

approved