A334879 a(1) = 1; a(n) = -(1/2) * Sum_{d|n, d > 1} d * (d + 1) * a(n/d).

1, -3, -6, -1, -15, 15, -28, -3, -9, 35, -66, 6, -91, 63, 60, -9, -153, 27, -190, 15, 105, 143, -276, 21, -100, 195, -54, 28, -435, -75, -496, -27, 231, 323, 210, 18, -703, 399, 312, 55, -861, -105, -946, 66, 135, 575, -1128, 72, -441, 300, 510, 91, -1431, 189, 440

Offset

1,2

Comments

Dirichlet inverse of the positive triangular numbers A000217.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} A000217(k) * A(x^k).

Dirichlet g.f.: 2 / (zeta(s-1) + zeta(s-2)).

Mathematica

a[n_] := If[n == 1, n, -(1/2) Sum[If[d > 1, d (d + 1) a[n/d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 55}]

Prog

(PARI) lista(nn) = {my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] =  -sumdiv(n, d, if (d>1, d*(d + 1)*va[n/d]))/2; ); va; } \\ Michel Marcus, May 15 2020

Crossrefs

Cf. A000217, A055615, A334657.

Sequence in context: A228335 A138799 A321480 * A108441 A176231 A176230

Adjacent sequences: A334876 A334877 A334878 * A334880 A334881 A334882

Keyword

sign

Author

Ilya Gutkovskiy, May 14 2020

Status

approved