A364066 Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-1)).

1, 2, 4, 4, 6, 6, 10, 8, 10, 10, 15, 14, 14, 14, 20, 16, 20, 18, 28, 20, 22, 24, 30, 24, 26, 30, 40, 28, 30, 30, 40, 34, 39, 34, 48, 36, 44, 38, 50, 46, 42, 44, 58, 44, 46, 46, 74, 52, 50, 50, 68, 54, 54, 62, 70, 56, 66, 58, 82, 60, 76, 64, 80, 64, 66, 66, 97, 78, 70, 74, 90, 74, 74, 80, 114, 76, 88, 78, 100

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/3) * Sum_{d | 3*n-1, d==2 (mod 3)} (d+1).

G.f.: Sum_{k>0} x^(2*k-1) / (1 - x^(3*k-2))^2.

Mathematica

a[n_] := DivisorSum[3*n - 1, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)

Prog

(PARI) a(n) = sumdiv(3*n-1, d, (d%3==2)*(d+1))/3;

Crossrefs

Cf. A364063, A364085.

Cf. A359211, A363890.

Sequence in context: A111457 A161765 A232091 * A164798 A087554 A281072

Adjacent sequences: A364063 A364064 A364065 * A364067 A364068 A364069

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved