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A109663 Numbers k such that the sum of the digits of (k^k + k!) is divisible by k. 1

%I #14 Jul 31 2022 07:43:41

%S 1,2,3,9,15,18,27,36,51,81,93,169,181,348,444,504,528,1881,2031,9843,

%T 16479,16685,45435,129056,138510,214008,358326

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

%C 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.

%C No more terms < 500000. - _Lars Blomberg_, Jul 05 2011

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

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

%t Select[Range[360000],Divisible[Total[IntegerDigits[#^#+#!]],#]&] (* _Harvey P. Dale_, Dec 27 2018 *)

%Y Cf. A053042, A109662.

%K base,more,nonn

%O 1,2

%A _Ryan Propper_, Aug 06 2005

%E a(21)-a(27) from _Lars Blomberg_, Jul 05 2011

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)