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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A134681, A034690.

Sequence in context: A117987 A091136 A140651 * A184392 A007955 A324502

Adjacent sequences: A190994 A190995 A190996 * A190998 A190999 A191000

Keyword

nonn,easy,base

Author

Jaroslav Krizek, Jun 15 2011

Status

approved