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

1,2

Links

Table of n, a(n) for n=1..39.

Example

9 is a term because the sum of the digits of 3^9 * 9! = 7142567040 is 36 which is divisible by 9.

Mathematica

Do[If[Mod[Plus @@ IntegerDigits[3^n * n!], n] == 0, Print[n]], {n, 1, 10000}]

Prog

(PARI) isok(k) = !(sumdigits(3^k * k!) % k);

Crossrefs

Cf. A032031, A007953, A052673, A108861.

Sequence in context: A036215 A103828 A110740 * A042938 A206604 A084707

Adjacent sequences: A348552 A348553 A348554 * A348556 A348557 A348558

Keyword

nonn,base,hard

Author

Kevin P. Thompson, Oct 21 2021

Extensions

a(36)-a(39) from Martin Ehrenstein, Nov 19 2021

Status

approved