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

%I A118541 #21 Jul 26 2018 06:59:32
%S A118541 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,
%T A118541 28,18,30,3,32,3,14,35,36,21,18,9,40,4,42,12,4,45,12,28,48,49,50,21,
%U A118541 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
%N A118541 Product of digits of prime factors of n, with multiplicity.
%C A118541 See also: A007954 Product of digits of n. See also: A118503 Sum of digits of prime factors of n, with multiplicity.
%H A118541 G. C. Greubel, <a href="/A118541/b118541.txt">Table of n, a(n) for n = 0..1000</a>
%F A118541 Completely multiplicative with a(p) = A007954(p) for prime p.
%e A118541 a(22) = 2 because 22 = 2 * 11 and the digital product of 2 * the digital product of 11 = 2 * ! * 1 = 2.
%e A118541 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.
%t A118541 Table[Times @@ Flatten@ Map[IntegerDigits, Table[#1, {#2}] & @@@ FactorInteger@ n], {n, 0, 78}] (* _Michael De Vlieger_, Jun 16 2016 *)
%o A118541 (PARI) \\ here b(n) is A007954.
%o A118541 b(n)={my(v=digits(n)); prod(i=1, #v, v[i])}
%o A118541 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
%Y A118541 Cf. A001221, A001222, A007953, A007954, A095402, A118503.
%K A118541 base,easy,nonn,mult
%O A118541 0,3
%A A118541 _Jonathan Vos Post_, May 06 2006
%E A118541 a(36) corrected by _Giovanni Resta_, Jun 16 2016
%E A118541 Keyword:mult added by _Andrew Howroyd_, Jul 23 2018