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a(n) = denominator of Sum_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k (A007955) and tau(k) = the number of the divisors of k (A000005).
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%I #16 Sep 08 2022 08:46:24

%S 1,1,2,3,2,2,2,3,2,2,2,6,2,2,4,15,2,2,2,2,4,2,2,6,6,2,4,6,2,4,2,5,4,2,

%T 4,6,2,2,4,2,2,4,2,2,4,2,2,30,6,2,4,6,2,4,4,6,4,2,2,4,2,2,4,35,4,4,2,

%U 2,4,4,2,6,2,2,12,6,4,4,2,10,20,2,2,12,4

%N a(n) = denominator of Sum_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k (A007955) and tau(k) = the number of the divisors of k (A000005).

%C Sum_{d|n} (pod(d)/tau(d)) > 1 for all n > 1.

%H Antti Karttunen, <a href="/A324983/b324983.txt">Table of n, a(n) for n = 1..20000</a>

%F a(p) = 2 for p = odd primes.

%e Sum_{d|n} (pod(d)/tau(d)) for n >= 1: 1, 2, 5/2, 14/3, 7/2, 25/2, 9/2, 62/3, 23/2, 59/2, ...

%e For n=4; Sum_{d|4} (pod(d)/tau(d)) = pod(1)/tau(1) + pod(2)/tau(2) + pod(4)/tau(4) = 1/1 + 2/2 + 8/3 = 14/3; a(4) = 3.

%t Array[Denominator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[0, #] &] &, 85] (* _Michael De Vlieger_, Mar 24 2019 *)

%o (Magma) [Denominator(&+[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]

%o (PARI) a(n) = denominator(sumdiv(n, d, vecprod(divisors(d))/numdiv(d))); \\ _Michel Marcus_, Mar 23 2019

%Y Cf. A000203, A007955, A324982 (numerators).

%K nonn,frac

%O 1,3

%A _Jaroslav Krizek_, Mar 22 2019