OFFSET
1,2
FORMULA
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).
Denominators of coefficients in expansion of -log(Product_{k>=1} (1 - x^k)^tau(k)), where tau(k) = number of divisors of k (A000005).
a(n) = denominator of Sum_{d|n} sigma(d)/d.
a(n) = denominator of (1/n)*Sum_{d|n} d*tau(d).
EXAMPLE
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, ...
MATHEMATICA
Denominator[Table[Sum[DivisorSigma[-1, d], {d, Divisors[n]}], {n, 75}]]
Denominator[Table[Sum[DivisorSigma[1, d]/d, {d, Divisors[n]}], {n, 75}]]
Denominator[Table[Sum[d DivisorSigma[0, d], {d, Divisors[n]}]/n, {n, 75}]]
nmax = 75; Rest[Denominator[CoefficientList[Series[Sum[DivisorSigma[1, k] x^k/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x]]]
nmax = 75; Rest[Denominator[CoefficientList[Series[-Log[Product[(1 - x^k)^DivisorSigma[0, k], {k, 1, nmax}]], {x, 0, nmax}], x]]]
PROG
(PARI) a(n) = denominator(sumdiv(n, d, sumdiv(d, j, 1/j))); \\ Michel Marcus, Aug 28 2018
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, Aug 27 2018
STATUS
approved