A363642 Expansion of Sum_{k>0} x^k/(1 - k*x^k)^3.

1, 4, 7, 17, 16, 55, 29, 129, 100, 311, 67, 1135, 92, 1919, 1486, 5409, 154, 17038, 191, 33491, 20938, 67871, 277, 262861, 9701, 373127, 296110, 978727, 436, 3134821, 497, 5051969, 3898522, 10027655, 474146, 39352069, 704, 49808159, 48362926, 127403221, 862, 411286429, 947

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+1,2).

Mathematica

a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + 1, 2] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+1, 2));

Crossrefs

Cf. A363639, A363643, A363644.

Cf. A167531, A363645.

Cf. A007437, A363650.

Sequence in context: A182929 A361733 A367744 * A124402 A349610 A216552

Adjacent sequences: A363639 A363640 A363641 * A363643 A363644 A363645

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved