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