A110728 Digital factorial: a(0) = 1, a(n) = n * (the sum of the digits of a(n-1)).

1, 1, 2, 6, 24, 30, 18, 63, 72, 81, 90, 99, 216, 117, 126, 135, 144, 153, 162, 171, 180, 189, 396, 414, 216, 225, 234, 243, 252, 261, 270, 279, 576, 594, 612, 315, 324, 333, 342, 351, 360, 369, 756, 774, 792, 810, 414, 423, 432, 441, 450, 459, 936, 954, 972

Offset: 0

Author

Amarnath Murthy, Aug 09 2005

Keywords

• base
• easy
• nonn

Examples

			a(4) = 24, a(5) = 5*(2+4) = 30, a(6) = 6*3 = 18.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000142, A007953, A089718, A110729.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      n*add(i, i=convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 12 2020

Mathematica

DigitSum[n_, 10] := Total[IntegerDigits[n, 10]]; A110728[0] := 1; A110728[n_] := A110728[n] = n*DigitSum[A110728[n - 1], 10]; Table[A110728[n], {n, 0, 50}] (* G. C. Greubel, Sep 06 2017 *)

PARI

s=vector(1001, n, 1); for(n=2, #s, s[n]=(n-1)*sumdigits(s[n-1])); s \\ Colin Barker, Nov 20 2014

Extensions

a(22) and a(32) corrected, name clarified, and more terms added by Colin Barker, Nov 20 2014