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A265709 a(n) = numerator of Sum_{d|n} 1/sigma(d).

%I A265709 #15 Feb 06 2024 08:13:27
%S A265709 1,4,5,31,7,5,9,54,69,14,13,155,15,3,35,1709,19,23,21,31,45,13,25,27,
%T A265709 223,10,703,93,31,35,33,15536,65,38,21,713,39,7,75,9,43,15,45,403,161,
%U A265709 25,49,1709,521,446,95,155,55,703,91,243,21,62,61,155,63,11
%N A265709 a(n) = numerator of Sum_{d|n} 1/sigma(d).
%C A265709 a(n) = numerator of Sum_{d|n} 1/A000203(d).
%C A265709 Are there numbers n > 1 such that Sum_{d|n} 1/sigma(d) is an integer?
%H A265709 Antti Karttunen, <a href="/A265709/b265709.txt">Table of n, a(n) for n = 1..16384</a>
%F A265709 a(n) = A265710(n) * Sum_{d|n} 1/sigma(d) = A265708(n) * A265710(n) / A069934(n).
%F A265709 a(1) = 1; a(p) = p + 2 for p = prime.
%e A265709 For n = 6; divisors d of 6: {1, 2, 3, 6}; sigma(d): {1, 3, 4, 12}; Sum_{d|6} 1/sigma(d) = 1/1 + 1/3 + 1/4 + 1/12 = 20/12 = 5/3; a(n) = 5.
%t A265709 A265709[n_] := Numerator[DivisorSum[n, 1/DivisorSigma[1,#]&]];
%t A265709 Array[A265709, 100] (* _Paolo Xausa_, Feb 06 2024 *)
%o A265709 (Magma) [Numerator(&+[1/SumOfDivisors(d): d in Divisors(n)]): n in [1..1000]]
%o A265709 (PARI) A265709(n) = numerator(sumdiv(n,d,1/sigma(d))); \\ _Antti Karttunen_, Nov 19 2017
%Y A265709 Cf. A069934, A000203, A265708, A265710, A265711, A265712, A265713, A265714, A266227, A266228.
%K A265709 nonn,frac
%O A265709 1,2
%A A265709 _Jaroslav Krizek_, Dec 24 2015