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%I #13 Sep 08 2022 08:46:24
%S 1,3,2,7,3,9,4,105,26,81,6,98,7,36,36,651,9,507,10,1323,64,81,12,
%T 11025,31,441,260,784,15,6561,16,13671,144,729,144,753571,19,225,196,
%U 893025,21,20736,22,2646,2028,324,24,423801,76,25947,324,16807,27,38025,324
%N a(n) = numerator of Product_{d|n} (sigma(d)/tau(d)) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
%C Product_{d|n} (sigma(d)/tau(d)) >= 1 for all n >= 1.
%F a(p) = (p+1)/2 for odd primes p.
%e Product_{d|n} (sigma(d)/tau(d)) for n >= 1: 1, 3/2, 2, 7/2, 3, 9, 4, 105/8, 26/3, 81/4, 6, 98, 7, 36, 36, 651/8, ...
%e For n=4; Product_{d|4} (sigma(d)/tau(d)) = sigma(1)/tau(1) + sigma(2)/tau(2) + sigma(4)/tau(4) = (1/1) * (3/2) * (7/3) = 7/2; a(4) = 7.
%t Table[Numerator[Product[DivisorSigma[1, k]/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 60}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Numerator(&*[SumOfDivisors(d) / NumberOfDivisors(d): d in Divisors(n)]): n in [1..60]]
%o (Sage) [product(sigma(k,1)/sigma(k,0) for k in n.divisors()).numerator() for n in (1..60)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A000005, A000203, A324510 (denominators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 03 2019
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