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

1,2

Links

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

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

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 *)

Crossrefs

Cf. A000045, A005086.

Sequence in context: A175028 A248006 A197699 * A136195 A117892 A286098

Adjacent sequences: A005089 A005090 A005091 * A005093 A005094 A005095

Keyword

nonn

Author

N. J. A. Sloane

Status

approved