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%I #17 Dec 24 2022 03:44:45
%S 1,2,6,4,120,12,5040,8,36,240,39916800,24,6227020800,10080,720,16,
%T 355687428096000,72,121645100408832000,480,30240,79833600,
%U 25852016738884976640000,48,14400,12454041600,216,20160,8841761993739701954543616000000,1440
%N Product of factorials of prime divisors of n (with multiplicity).
%H Alois P. Heinz, <a href="/A240023/b240023.txt">Table of n, a(n) for n = 1..300</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F Completely multiplicative with a(p) = p!.
%F Sum_{n>=1} 1/a(n) = 1/Product_{p prime} (1 - 1/p!) = 2.42064841562992124691... . - _Amiram Eldar_, Dec 24 2022
%p a:= n-> mul(i[1]!^i[2], i=ifactors(n)[2]):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Mar 30 2014
%t f[p_, e_] := p!^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* _Amiram Eldar_, Aug 04 2022 *)
%o (PARI) a(n)=local(fm=factor(n));prod(k=1,matsize(fm)[1],fm[k,1]!^fm[k,2])
%Y Cf. A000142.
%K nonn,mult
%O 1,2
%A _Franklin T. Adams-Watters_, Mar 30 2014
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