A005092 Sum of Fibonacci numbers 1,2,3,5,... that divide n.

1, 3, 4, 3, 6, 6, 1, 11, 4, 8, 1, 6, 14, 3, 9, 11, 1, 6, 1, 8, 25, 3, 1, 14, 6, 16, 4, 3, 1, 11, 1, 11, 4, 37, 6, 6, 1, 3, 17, 16, 1, 27, 1, 3, 9, 3, 1, 14, 1, 8, 4, 16, 1, 6, 61, 11, 4, 3, 1, 11, 1, 3, 25, 11, 19, 6, 1, 37, 4, 8, 1, 14, 1, 3, 9, 3, 1, 19, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000045, A005086.

Programs

Maple

a:= n-> add(`if`(issqr(5*d^2+4) or issqr(5*d^2-4), d, 0)
        , d=numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 07 2017

Mathematica

nmax = 100; With[{fibs = Fibonacci[Range[2, Floor[Log[nmax*Sqrt[5]] / Log[GoldenRatio]] + 1]]}, Table[Total[Select[fibs, Divisible[n, #1] & ]], {n, 1, nmax}]] (* Vaclav Kotesovec, Apr 29 2019 *)

Formula

G.f.: Sum_{k>=2} F(k)*x^F(k)/(1 - x^F(k)), where F(k) is the k-th Fibonacci number (A000045). - Ilya Gutkovskiy, Jan 06 2017