A034772 - OEIS

%I #10 Sep 11 2019 05:16:45

%S 1,3,4,8,7,18,15,34,41,71,91,182,235,409,628,1047,1599,2685,4183,6906,

%T 10980,17895,28659,46756,75038,121865,196496,318620,514231,833426,

%U 1346271,2180369,3524764,5706087,9227505,14935978,24157819,39096537

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

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

%F a(n) ~ ((1+sqrt(5))/2)^n / sqrt(5). - _Vaclav Kotesovec_, Sep 11 2019

%t Table[Sum[Fibonacci[n/d]*DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 40}] (* _Vaclav Kotesovec_, Sep 10 2019 *)

%Y Cf. A000005, A000045.

%K nonn

%O 1,2

%A _Erich Friedman_