A034772 Dirichlet convolution of d(n) (number of divisors) with Fibonacci numbers.

1, 3, 4, 8, 7, 18, 15, 34, 41, 71, 91, 182, 235, 409, 628, 1047, 1599, 2685, 4183, 6906, 10980, 17895, 28659, 46756, 75038, 121865, 196496, 318620, 514231, 833426, 1346271, 2180369, 3524764, 5706087, 9227505, 14935978, 24157819, 39096537

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Formula

G.f.: Sum_{k>=1} d(k) * x^k/(1 - x^k - x^(2*k)). - Ilya Gutkovskiy, Jul 23 2019

a(n) ~ ((1+sqrt(5))/2)^n / sqrt(5). - Vaclav Kotesovec, Sep 11 2019

Mathematica

Table[Sum[Fibonacci[n/d]*DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 40}] (* Vaclav Kotesovec, Sep 10 2019 *)

Crossrefs

Cf. A000005, A000045.

Sequence in context: A310014 A310015 A123323 * A197138 A065309 A097689

Adjacent sequences: A034769 A034770 A034771 * A034773 A034774 A034775

Keyword

nonn

Author

Erich Friedman

Status

approved