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%I #8 Mar 02 2024 03:50:45
%S 1,1,1,2,1,1,1,2,3,1,1,2,1,1,1,2,1,3,1,2,1,1,1,2,5,1,3,2,1,1,1,2,1,1,
%T 1,1,1,1,1,2,1,1,1,2,3,1,1,2,7,5,1,2,1,3,1,2,1,1,1,2,1,1,3,2,1,1,1,2,
%U 1,1,1,1,1,1,5,2,1,1,1,2,3,1,1,2,1,1,1
%N a(n) is the denominator of the sum of the reciprocals of the squarefree divisors of the powerful part of n.
%H Amiram Eldar, <a href="/A370784/b370784.txt">Table of n, a(n) for n = 1..10000</a>
%H Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.12174.13124">Arithmetical Functions over the Powerful Part of an Integer</a>, ResearchGate, 2024.
%F a(n) = A332881(A057521(n)).
%F a(n) = 1 if n is squarefree (A005117).
%t a[n_] := Denominator[Times @@ (1 + 1/Select[FactorInteger[n], Last[#] > 1 &][[;; , 1]])]; Array[a, 100]
%o (PARI) a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, if(f[i,2] == 1, 1, 1 + 1/f[i,1])));}
%Y Cf. A005117, A057521, A295295, A332881, A370783 (numerators).
%K nonn,easy,frac
%O 1,4
%A _Amiram Eldar_, Mar 02 2024