A076428 Numbers k such that the sum of digits of k in superfactorial base divides k.

1, 2, 4, 6, 8, 10, 12, 14, 15, 20, 24, 28, 30, 36, 40, 42, 48, 50, 56, 60, 63, 70, 72, 80, 84, 90, 96, 100, 108, 110, 120, 121, 132, 144, 150, 153, 156, 168, 180, 192, 200, 204, 216, 220, 228, 231, 240, 250, 252, 264, 276, 288, 290, 291, 295, 300, 304, 305, 312, 315

Offset: 1

Author

Floor van Lamoen, Oct 10 2002

Keywords

• nonn
• base

Comments

We define the superfactorial base as a variant of the factorial base where place values are superfactorials (A000178) instead of factorials (A000142). - Rémy Sigrist, Mar 20 2018

Examples

			28 written in superfactorial base is 220, the sum of digits is thus 4 and 4 divides 28, so 28 is included in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000142, A000178, A118363.

Programs

Maple

A076428 := proc(n) local i,j,m,t,t1; t := NULL; for j from 1 to n do m := j; i := 2; t1 := 0; while m>0 do t1 := t1 + (m mod i!); m := floor(m/i!); i := i+1; od; if j mod t1 = 0 then t := t,j fi; od; t; end;

Mathematica

max = 4; bases = Range[max, 1, -1]!; nmax = Times @@ bases - 1; sumdig[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; Select[Range[nmax], Divisible[#, sumdig[#]] &] (* Amiram Eldar, Sep 07 2020 *)

Extensions

Definition corrected by Rémy Sigrist, Mar 20 2018