A363641 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^2.

0, 1, 2, 4, 4, 10, 6, 20, 14, 42, 10, 127, 12, 206, 132, 512, 16, 1459, 18, 2655, 1492, 5142, 22, 17795, 524, 24602, 17540, 59567, 28, 177776, 30, 274656, 196884, 524322, 20156, 1901506, 36, 2359334, 2125828, 5682323, 40, 17453224, 42, 24641943, 22948512, 46137390, 46

Offset

1,3

Links

Table of n, a(n) for n=1..47.

Formula

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

If p is prime, a(p) = p - 1.

Mathematica

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

Prog

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

Crossrefs

Cf. A167531, A362683.

Cf. A363649.

Sequence in context: A038043 A126138 A366575 * A247570 A054764 A267311

Adjacent sequences: A363638 A363639 A363640 * A363642 A363643 A363644

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved