%I #12 Sep 08 2022 08:46:24
%S 1,3,4,21,6,12,8,105,52,18,12,84,14,24,24,3255,18,156,20,126,32,36,24,
%T 420,186,42,520,168,30,72,32,9765,48,54,48,156,38,60,56,70,42,96,44,
%U 252,312,72,48,13020,456,558,72,294,54,1560,72,840,16,90,60,504
%N a(n) = denominator of Sum_{d|n} (pod(d)/sigma(d)) where pod(k) = the product of the divisors of k (A007955) and sigma(k) = the sum of the divisors of k (A000203).
%C Sum_{d|n} (pod(d)/tau(d)) > 1 for all n > 1.
%e For n=4; Sum_{d|4} (pod(d)/sigma(d)) = pod(1)/sigma(1) + pod(2)/sigma(2) + pod(4)/sigma(4) = 1/1 + 2/3 + 8/7 = 59/21; a(4) = 21.
%t Array[Denominator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[1, #] &] &, 60] (* _Michael De Vlieger_, Mar 24 2019 *)
%o (Magma) [Denominator(&+[&*[c: c in Divisors(d)] / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = denominator(sumdiv(n,d, vecprod(divisors(d))/sigma(d))); \\ _Michel Marcus_, Mar 23 2019
%Y Cf. A000203, A007955, A324984 (numerators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 22 2019