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%I #13 Apr 29 2019 03:53:22
%S 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,
%T 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,
%U 1,3,25,11,19,6,1,37,4,8,1,14,1,3,9,3,1,19,1
%N Sum of Fibonacci numbers 1,2,3,5,... that divide n.
%H Alois P. Heinz, <a href="/A005092/b005092.txt">Table of n, a(n) for n = 1..20000</a>
%F 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
%p a:= n-> add(`if`(issqr(5*d^2+4) or issqr(5*d^2-4), d, 0)
%p , d=numtheory[divisors](n)):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jan 07 2017
%t 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 *)
%Y Cf. A000045, A005086.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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