%I #6 Aug 28 2018 05:58:03

%S 1,2,3,4,5,6,7,8,9,2,11,12,13,14,15,16,17,9,19,20,1,22,23,24,25,26,27,

%T 28,29,6,31,32,33,34,7,18,37,38,13,40,41,2,43,44,45,46,47,16,49,5,51,

%U 52,53,27,5,8,19,58,59,60,61,62,21,64,65,66,67,4,69,14,71,36,73,74,75

%N a(n) is the denominator of Sum_{d|n} Sum_{j|d} 1/j.

%F Denominators of coefficients in expansion of Sum_{k>=1} sigma(k)*x^k/(k*(1 - x^k)), where sigma(k) = sum of divisors of k (A000203).

%F Denominators of coefficients in expansion of -log(Product_{k>=1} (1 - x^k)^tau(k)), where tau(k) = number of divisors of k (A000005).

%F a(n) = denominator of Sum_{d|n} sigma(d)/d.

%F a(n) = denominator of (1/n)*Sum_{d|n} d*tau(d).

%e 1, 5/2, 7/3, 17/4, 11/5, 35/6, 15/7, 49/8, 34/9, 11/2, 23/11, 119/12, 27/13, 75/14, 77/15, 129/16, ...

%t Denominator[Table[Sum[DivisorSigma[-1, d], {d, Divisors[n]}], {n, 75}]]

%t Denominator[Table[Sum[DivisorSigma[1, d]/d, {d, Divisors[n]}], {n, 75}]]

%t Denominator[Table[Sum[d DivisorSigma[0, d], {d, Divisors[n]}]/n, {n, 75}]]

%t nmax = 75; Rest[Denominator[CoefficientList[Series[Sum[DivisorSigma[1, k] x^k/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x]]]

%t nmax = 75; Rest[Denominator[CoefficientList[Series[-Log[Product[(1 - x^k)^DivisorSigma[0, k], {k, 1, nmax}]], {x, 0, nmax}], x]]]

%o (PARI) a(n) = denominator(sumdiv(n, d, sumdiv(d, j, 1/j))); \\ _Michel Marcus_, Aug 28 2018

%Y Cf. A000005, A000203, A006171, A007429, A017665, A017666, A060640, A068986 (positions of 1's), A318491 (numerators).

%K nonn,frac

%O 1,2

%A _Ilya Gutkovskiy_, Aug 27 2018