A334890 a(1) = 1; a(n) = -Sum_{d|n, d > 1} (sigma(d) - d) * a(n/d).

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

Links

Table of n, a(n) for n=1..65.

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

Cf. A000203, A001065, A046692, A305807.

Sequence in context: A105498 A179289 A083414 * A171174 A171173 A268671

Adjacent sequences: A334887 A334888 A334889 * A334891 A334892 A334893

Keyword

sign

Author

Ilya Gutkovskiy, May 14 2020

Status

approved