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

1,2

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000142, A000178, A118363.

Sequence in context: A184592 A247427 A316837 * A319747 A055958 A241142

Adjacent sequences: A076425 A076426 A076427 * A076429 A076430 A076431

Keyword

nonn,base

Author

Floor van Lamoen, Oct 10 2002

Extensions

Definition corrected by Rémy Sigrist, Mar 20 2018

Status

approved