A307777 a(1) = 1; a(n+1) = Sum_{d|n} (-1)^(n/d+d)*a(d).

1, 1, -2, -1, 1, 2, -2, -1, 0, -1, -2, -1, 6, 7, -7, -7, 5, 6, -8, -7, 6, 3, -3, -2, 5, 7, -15, -16, 26, 27, -22, -21, 12, 9, -16, -16, 28, 29, -23, -18, 9, 10, -23, -22, 28, 21, -20, -19, 25, 24, -31, -27, 29, 30, -23, -23, 16, 7, -35, -34, 79, 80, -60, -57, 27, 35, -50, -49, 54, 50, -41

Offset

1,3

Links

Table of n, a(n) for n=1..71.

Formula

G.f.: x * (1 - Sum_{n>=1} a(n)*(-x)^n/(1 + x^n)).

L.g.f.: log(Product_{n>=1} (1 + x^n)^((-1)^(n+1)*a(n)/n)) = Sum_{n>=1} a(n+1)*x^n/n.

Mathematica

a[n_] := a[n] = Sum[(-1)^((n - 1)/d + d) a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 71}]
a[n_] := a[n] = SeriesCoefficient[x (1 - Sum[a[k] (-x)^k/(1 + x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 71}]

Crossrefs

Cf. A003238, A281487, A307776, A307778, A307779.

Sequence in context: A171532 A171533 A115236 * A365661 A284593 A190672

Adjacent sequences: A307774 A307775 A307776 * A307778 A307779 A307780

Keyword

sign

Author

Ilya Gutkovskiy, Apr 28 2019

Status

approved