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A332881 If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j).

%I A332881 #14 Nov 15 2021 13:01:56
%S A332881 1,2,3,2,5,1,7,2,3,5,11,1,13,7,5,2,17,1,19,5,21,11,23,1,5,13,3,7,29,5,
%T A332881 31,2,11,17,35,1,37,19,39,5,41,7,43,11,5,23,47,1,7,5,17,13,53,1,55,7,
%U A332881 57,29,59,5,61,31,21,2,65,11,67,17,23,35
%N A332881 If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j).
%C A332881 Denominator of sum of reciprocals of squarefree divisors of n.
%H A332881 Antti Karttunen, <a href="/A332881/b332881.txt">Table of n, a(n) for n = 1..20000</a>
%F A332881 Denominators of coefficients in expansion of Sum_{k>=1} mu(k)^2*x^k/(k*(1 - x^k)).
%F A332881 a(n) = denominator of Sum_{d|n} mu(d)^2/d.
%F A332881 a(n) = denominator of psi(n)/n.
%F A332881 a(p) = p, where p is prime.
%F A332881 a(n) = n / A306695(n) = n / gcd(n, A001615(n)). - _Antti Karttunen_, Nov 15 2021
%e A332881 1, 3/2, 4/3, 3/2, 6/5, 2, 8/7, 3/2, 4/3, 9/5, 12/11, 2, 14/13, 12/7, 8/5, 3/2, 18/17, ...
%p A332881 a:= n-> denom(mul(1+1/i[1], i=ifactors(n)[2])):
%p A332881 seq(a(n), n=1..80);  # _Alois P. Heinz_, Feb 28 2020
%t A332881 Table[If[n == 1, 1, Times @@ (1 + 1/#[[1]] & /@ FactorInteger[n])], {n, 1, 70}] // Denominator
%t A332881 Table[Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}], {n, 1, 70}] // Denominator
%o A332881 (PARI)
%o A332881 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A332881 A332881(n) = denominator(A001615(n)/n);
%Y A332881 Cf. A001615, A008683, A017666, A048250, A007947, A109395, A187778 (positions of 1's), A306695, A308443, A308462, A332880 (numerators), A332883.
%K A332881 nonn,frac
%O A332881 1,2
%A A332881 _Ilya Gutkovskiy_, Feb 28 2020