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A005092 Sum of Fibonacci numbers 1,2,3,5,... that divide n. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 25 07:29 EST 2020. Contains 331241 sequences. (Running on oeis4.)