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A334879
a(1) = 1; a(n) = -(1/2) * Sum_{d|n, d > 1} d * (d + 1) * a(n/d).
1
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
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 14 2020
STATUS
approved