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A066769 a(n) = Sum_{d|n} d*Fibonacci(n/d).

%I A066769 #16 Sep 16 2020 05:01:48
%S A066769 1,3,5,9,10,21,20,39,49,80,100,195,246,424,650,1065,1614,2715,4200,
%T A066769 6940,11020,17922,28680,46821,75075,121898,196565,318680,514258,
%U A066769 833560,1346300,2180439,3524900,5706132,9227600,14936241,24157854,39096588
%N A066769 a(n) = Sum_{d|n} d*Fibonacci(n/d).
%C A066769 Dirichlet convolution of f(n)=n with the Fibonacci numbers F(n)=A000045. See the Apostol reference for Dirichlet convolutions. - _Wolfdieter Lang_, Sep 09 2008
%D A066769 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, pp. 29 ff.
%H A066769 Robert Israel, <a href="/A066769/b066769.txt">Table of n, a(n) for n = 1..4740</a>
%F A066769 G.f.: Sum_{i>0} i*x^i/(1-x^i-x^(2*i)). - _Vladeta Jovovic_, Oct 06 2003
%p A066769 N:= 100:
%p A066769 A:= Vector(N):
%p A066769 for k from 1 to N do
%p A066769   f:= combinat:-fibonacci(k);
%p A066769   ds:= [$1..floor(N/k)];
%p A066769   A[k*ds] := A[k*ds] + f*Vector(ds);
%p A066769 od:
%p A066769 convert(A,list); # _Robert Israel_, Feb 08 2016
%t A066769 a[n_] := DivisorSum[n, # * Fibonacci[n/#] &]; Array[a, 38] (* _Amiram Eldar_, Sep 16 2020 *)
%o A066769 (PARI) a(n) = sumdiv(n, d, d*fibonacci(n/d)); \\ _Michel Marcus_, Sep 16 2020
%Y A066769 Cf. A000045, A007435.
%K A066769 easy,nonn
%O A066769 1,2
%A A066769 _Vladeta Jovovic_, Jan 17 2002