A348555 Numbers k that divide the sum of the digits of 3^k * k!.
1, 3, 9, 27, 72, 111, 129, 148, 161, 450, 762, 1233, 1260, 2052, 9153, 15840, 16067, 16302, 16317, 16332, 16435, 74670, 74946, 125046, 208566, 347670, 347685, 583263, 1609667, 1610942, 1616476, 1616532, 1616958, 2683143, 2700261, 4480092, 7469682, 7470432, 7492497
Offset: 1
Examples
9 is a term because the sum of the digits of 3^9 * 9! = 7142567040 is 36 which is divisible by 9.
Programs
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Mathematica
Do[If[Mod[Plus @@ IntegerDigits[3^n * n!], n] == 0, Print[n]], {n, 1, 10000}] -
PARI
isok(k) = !(sumdigits(3^k * k!) % k);
Extensions
a(36)-a(39) from Martin Ehrenstein, Nov 19 2021