

A118541


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


1



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
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OFFSET

0,3


COMMENTS

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


LINKS

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


FORMULA

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


EXAMPLE

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.


MATHEMATICA

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


PROG

(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


CROSSREFS

Cf. A001221, A001222, A007953, A007954, A095402, A118503.
Sequence in context: A203814 A280505 A262401 * A084905 A180409 A320485
Adjacent sequences: A118538 A118539 A118540 * A118542 A118543 A118544


KEYWORD

base,easy,nonn,mult


AUTHOR

Jonathan Vos Post, May 06 2006


EXTENSIONS

a(36) corrected by Giovanni Resta, Jun 16 2016
Keyword:mult added by Andrew Howroyd, Jul 23 2018


STATUS

approved



