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%I #19 Sep 08 2022 08:46:24
%S 1,2,1,6,1,2,1,12,3,1,1,2,1,2,1,60,1,3,1,3,1,2,1,4,3,1,3,6,1,1,1,60,1,
%T 1,1,9,1,2,1,3,1,2,1,6,3,2,1,20,1,6,1,3,1,3,1,12,1,1,1,1,1,2,3,420,1,
%U 2,1,3,1,1,1,18,1,1,1,6,1,1,1,15,15,1,1,2
%N a(n) = denominator 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 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.
%H Antti Karttunen, <a href="/A324500/b324500.txt">Table of n, a(n) for n = 1..20000</a>
%F a(p) = 1 for odd primes p.
%F a(n) = 1 for numbers in A306639.
%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) = 6.
%t Table[Denominator[Sum[DivisorSigma[1, k]/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 100}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Denominator(&+[SumOfDivisors(d) / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = denominator(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() ).denominator() for n in (1..100)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A000005, A000203, A323779, A323780, A323781, A324499 (numerators), A306639.
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 02 2019
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