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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 04:57 EDT 2019. Contains 328145 sequences. (Running on oeis4.)