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%I #13 Sep 08 2022 08:46:24
%S 1,5,7,59,11,65,15,743,199,145,23,5735,27,257,287,130553,35,24497,39,
%T 25159,525,577,47,2352899,1091,785,11467,67847,59,811525,63,5470699,
%U 1217,1297,1355,17310353,75,1601,1671,2005387,83,3114407,87,259879,368879,2305
%N a(n) = numerator 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)/sigma(d)) for n >= 1: 1, 5/3, 7/4, 59/21, 11/6, 65/12, 15/8, 743/105, ...
%C Sum_{d|n} (pod(d)/sigma(d)) > 1 for all n > 1.
%C a(p) = 2p + 1 for p = primes (A000040).
%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) = 59.
%t Array[Numerator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[1, #] &] &, 46] (* _Michael De Vlieger_, Mar 24 2019 *)
%o (Magma) [Numerator(&+[&*[c: c in Divisors(d)] / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = numerator(sumdiv(n,d, vecprod(divisors(d))/sigma(d))); \\ _Michel Marcus_, Mar 23 2019
%Y Cf. A000203, A007955, A324985 (denominators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 22 2019
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