A118541 Product of digits of prime factors of n, with multiplicity.

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 3, 14, 15, 16, 7, 18, 9, 20, 21, 2, 6, 24, 25, 6, 27, 28, 18, 30, 3, 32, 3, 14, 35, 36, 21, 18, 9, 40, 4, 42, 12, 4, 45, 12, 28, 48, 49, 50, 21, 12, 15, 54, 5, 56, 27, 36, 45, 60, 6, 6, 63, 64, 15, 6, 42, 28, 18, 70, 7, 72, 21, 42, 75, 36, 7, 18

Offset: 0

Author

Jonathan Vos Post, May 06 2006

Keywords

• base
• easy
• nonn
• mult

Comments

See also: A007954 Product of digits of n. See also: A118503 Sum of digits of prime factors of n, with multiplicity.

Examples

			a(22) = 2 because 22 = 2 * 11 and the digital product of 2 * the digital product of 11 = 2 * ! * 1 = 2.
a(121) = 1 because 121 = 11^2 = 11 * 11, multiplying the digits of the prime factors with multiplicity gives A007954(11) +A007954(11) = 1 * 1 = 1.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001221, A001222, A007953, A007954, A095402, A118503.

Programs

Mathematica

Table[Times @@ Flatten@ Map[IntegerDigits, Table[#1, {#2}] & @@@ FactorInteger@ n], {n, 0, 78}] (* Michael De Vlieger, Jun 16 2016 *)

PARI

\\ here b(n) is A007954.
b(n)={my(v=digits(n)); prod(i=1, #v, v[i])}
a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i,1], e=f[i,2]); b(p)^e)} \\ Andrew Howroyd, Jul 23 2018

Formula

Completely multiplicative with a(p) = A007954(p) for prime p.

Extensions

a(36) corrected by Giovanni Resta, Jun 16 2016

Keyword:mult added by Andrew Howroyd, Jul 23 2018