A128212 a(n) = Sum_digits(p), where p is the product of the digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 1, 3, 5, 7, 9, 0, 3, 6, 9, 3, 6, 9, 3, 6, 9, 0, 4, 8, 3, 7, 2, 6, 10, 5, 9, 0, 5, 1, 6, 2, 7, 3, 8, 4, 9, 0, 6, 3, 9, 6, 3, 9, 6, 12, 9, 0, 7, 5, 3, 10, 8, 6, 13, 11, 9, 0, 8, 7, 6, 5, 4, 12, 11, 10, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, May 03 2007

Keywords

• easy
• nonn
• base

Comments

The sequence grows very slowly. For n <= 10000 the maximal value is 27.

Examples

			a(73) = 3 because 7*3 = 21 and 2+1 = 3.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..6000

Crossrefs

Cf. A007953, A007954.

Programs

Magma

[&+Intseq((&*(Intseq(n)))):n in [1..100]]; // Marius A. Burtea, Jun 06 2019

Maple

P:=proc(n) local i,k,w; for i from 1 by 1 to n do w:=1;k:=i; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; k:=w; w:=0; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; print(w); od; end: P(100);

Mathematica

Table[Total[IntegerDigits[Times@@IntegerDigits[n]]],{n,100}] (* Harvey P. Dale, Feb 08 2013 *)

PARI

a(n) = sumdigits(vecprod(digits(n))); \\ Michel Marcus, Jun 07 2019

Formula

a(n) = A007953(A007954(n)). - Michel Marcus, Jun 07 2019 [Corrected by Sean A. Irvine, Sep 26 2023]