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%I #12 Sep 08 2022 08:46:24
%S 1,5,3,29,4,15,5,103,22,10,7,29,8,25,12,887,10,55,11,58,15,35,13,103,
%T 43,20,52,145,16,30,17,1517,21,25,20,319,20,55,24,103,22,75,23,203,88,
%U 65,25,887,24,215,30,116,28,130,28,515,33,40,31,58,32,85,110
%N a(n) = numerator of Sum_{d|n} sigma(d)/tau(d) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of the divisors of k (A000005).
%C Sum_{d|n} sigma(d)/tau(d) > 1 for all n > 1.
%C Sum_{d|n} sigma(d)/tau(d) = n only for numbers n = 1, 3, 10 and 30.
%e Sum_{d|n} sigma(d)/tau(d) for n >= 1: 1, 5/2, 3, 29/6, 4, 15/2, 5, 103/12, 22/3, 10, 7, 29/2, 8, 25/2, 12, 887/60, ...
%e For n=4; Sum_{d|4} sigma(d)/tau(d) = sigma(1)/tau(1) + sigma(2)/tau(2) + sigma(4)/tau(4) = 1/1 + 3/2 + 7/3 = 29/6; a(4) = 29.
%t Table[Numerator[Sum[DivisorSigma[1, k]/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 100}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Numerator(&+[SumOfDivisors(d) / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = numerator(sumdiv(n, d, sigma(d)/numdiv(d))); \\ _Michel Marcus_, Mar 03 2019
%o (Sage) [sum(sigma(k,1)/sigma(k,0) for k in n.divisors() ).numerator() for n in (1..100)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A000005, A000203, A323779, A323780, A323781, A324500 (denominators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 02 2019
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