OFFSET
0,5
FORMULA
a(n) = [x^n] 1/(1 - Sum_{k>=1} (sigma_n(k) - k^n)*x^k).
a(n) = [x^n] 1/(1 - Sum_{k>=1} (k^n - J_n(k))*x^k/(1 - x^k)), where J_() is the Jordan function.
MATHEMATICA
Table[SeriesCoefficient[1/(1 - Sum[k^n x^(2 k)/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - Sum[(DivisorSigma[n, k] - k^n) x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - Sum[(k^n - Sum[d^n MoebiusMu[k/d], {d, Divisors[k]}]) x^k/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 01 2018
STATUS
approved