A321261 -id:A321261 - cp's OEIS frontend

A321260 a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^(sigma_n(k)-k^n).

1, 0, 1, 1, 18, 2, 861, 132, 106024, 40910, 72980055, 6838271, 228282942581, 27620223647, 2050169324675668, 352809815149813, 87174966874755673105, 6798293425492905407, 18318448554980083512011863, 1187839217207171380193247, 11258918803635775614062752424535

Offset: 0

Ilya Gutkovskiy, Nov 01 2018

nonn

Cf. A283333, A318783, A318784, A319647, A321258, A321261.

Table[SeriesCoefficient[Product[1/(1 - x^k)^(DivisorSigma[n, k] - k^n), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[Exp[Sum[DivisorSigma[n + 1, k] x^(2 k)/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 20}]

a(n) = [x^n] exp(Sum_{k>=1} sigma_(n+1)(k)*x^(2*k)/(k*(1 - x^k))).

A321263 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^nx^(2k)/(1 - x^k)).

Original entry on oeis.org

1, 0, 1, 1, 18, 3, 926, 264, 146255, 64190, 138356840, 22816773, 509079790798, 108923489863, 6757117812676818, 1403337110700033, 474610323092906351464, 52144014892723916074, 130074987349483695192896881, 14487112805054799566652854, 132992779975091800967037313578152

Offset: 0

Ilya Gutkovskiy, Nov 01 2018

nonn

Cf. A321190, A321258, A321260, A321261, A321262.

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}]

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.

cp's OEIS Frontend

A321260 a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^(sigma_n(k)-k^n).

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Formula

A321263 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^nx^(2k)/(1 - x^k)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

A321260 a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^(sigma_n(k)-k^n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A321263 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^(2*k)/(1 - x^k)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A321263 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^nx^(2k)/(1 - x^k)).