A190997 Product of digits of all the divisors of n.

1, 2, 3, 8, 5, 36, 7, 64, 27, 0, 1, 288, 3, 56, 75, 384, 7, 2592, 9, 0, 42, 8, 6, 18432, 50, 72, 378, 3584, 18, 0, 3, 2304, 27, 168, 525, 373248, 21, 432, 243, 0, 4, 16128, 12, 512, 13500, 288, 28, 3538944, 252, 0, 105, 2880, 15, 725760, 125, 860160, 945

Offset: 1

Author

Jaroslav Krizek, Jun 15 2011

Keywords

• nonn
• easy
• base

Comments

Product of digits of concatenation of all divisors of n (A037278).

Examples

			For n = 12: a(12) = 1 * 2 * 3 * 4 * 6 * 1 * 2 = 288.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134681, A034690.

Programs

Maple

A190997:=proc(n) local d, i, p: d:=numtheory[divisors](n): p:=1: for i from 1 to nops(d) do p:=p*mul(d, d=convert(d[i], base, 10)): od: return p: end: seq(A190997(n),n=1..57); # Nathaniel Johnston, Jun 15 2011

Mathematica

Table[Times@@Flatten[IntegerDigits/@Divisors[n]],{n,100}] (* Harvey P. Dale, Nov 27 2022 *)

PARI

a007954(n) = my(d=digits(n)); prod(i=1, #d, d[i]);
a(n) = my(div=divisors(n), pdt=1); for(k=1, #div, pdt=pdt*a007954(div[k])); pdt \\ Felix Fröhlich, Sep 22 2016

Formula

a(n) = 0 for n = multiples of 10; a(A008592(n)) = 0 for n >=1.