%I #12 Jul 31 2022 07:43:36
%S 1,2,3,9,14,15,29,33,45,81,102,105,126,142,157,288,414,1184,2133,
%T 10449,16369,17221,46524,214179,216741
%N Numbers k such that the sum of the digits of (k^k - k!) is divisible by k.
%C 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.
%C No more terms < 500000. - _Lars Blomberg_, Jul 05 2011
%e The digits of 414^414 - 414! sum to 4968 and 4968 is divisible by 414, so 414 is in the sequence.
%t Do[s = n^n - n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]
%Y Cf. A036679, A109663.
%K base,more,nonn
%O 1,2
%A _Ryan Propper_, Aug 06 2005
%E Terms a(20)-a(25) from _Lars Blomberg_, Jul 05 2011
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