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A334890
a(1) = 1; a(n) = -Sum_{d|n, d > 1} (sigma(d) - d) * a(n/d).
0
1, -1, -1, -2, -1, -4, -1, -2, -3, -6, -1, -1, -1, -8, -7, 0, -1, -4, -1, -3, -9, -12, -1, 14, -5, -14, -6, -5, -1, -2, -1, 4, -13, -18, -11, 28, -1, -20, -15, 18, -1, -6, -1, -9, -10, -24, -1, 36, -7, -18, -19, -11, -1, 12, -15, 22, -21, -30, -1, 85, -1, -32, -14, 8, -17
OFFSET
1,4
FORMULA
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} A001065(k) * A(x^k).
Dirichlet g.f.: 1 / (1 + zeta(s-1) * (zeta(s) - 1)).
MATHEMATICA
a[n_] := If[n == 1, n, -Sum[If[d > 1, (DivisorSigma[1, d] - d) a[n/d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 65}]
PROG
(PARI) lista(nn) = {my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = -sumdiv(n, d, if (d>1, (sigma(d) - d) * va[n/d])); ); va; } \\ Michel Marcus, May 15 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 14 2020
STATUS
approved