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%I #14 Sep 08 2022 08:46:24
%S 1,2,3,8,5,36,7,64,27,100,11,1728,13,196,225,1024,17,5832,19,8000,441,
%T 484,23,331776,125,676,729,21952,29,810000,31,32768,1089,1156,1225,
%U 10077696,37,1444,1521,2560000,41,3111696,43,85184,91125,2116,47,254803968,343
%N a(n) = denominator of Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).
%C Sum_{d|n} (1/pod(d)) >= 1 for all n >= 1.
%C Is this a duplicate of A007955? - _R. J. Mathar_, Mar 28 2019
%F a(n) = n for noncomposite numbers n (A008578).
%e Sum_{d|n} (1/pod(d)) for n >= 1: 1, 3/2, 4/3, 13/8, 6/5, 67/36, 8/7, 105/64, 37/27, 171/100, 12/11, 3433/1728, ...
%e For n=4; Sum_{d|4} (1/pod(d)) = 1/pod(1) + 1/pod(2) + 1/pod(4) = (1/1) + (1/2) + (1/8) = 13/8; a(4) = 8.
%t Table[Denominator[Sum[Product[1/d , {d, Divisors[k]}], {k, Divisors[n]} ]], {n, 1, 50}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Denominator(&+[1 / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..50]]
%o (PARI) a(n) = denominator(sumdiv(n, d, 1/vecprod(divisors(d)))); \\ _Michel Marcus_, Mar 03 2019
%o (Sage) [sum(product(1/j for j in k.divisors()) for k in n.divisors() ).denominator() for n in (1..50)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A007955, A324501 (numerators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 02 2019
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