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A066769
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a(n) = Sum_{d|n} d*Fibonacci(n/d).
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1
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1, 3, 5, 9, 10, 21, 20, 39, 49, 80, 100, 195, 246, 424, 650, 1065, 1614, 2715, 4200, 6940, 11020, 17922, 28680, 46821, 75075, 121898, 196565, 318680, 514258, 833560, 1346300, 2180439, 3524900, 5706132, 9227600, 14936241, 24157854, 39096588
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, pp. 29 ff.
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LINKS
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FORMULA
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MAPLE
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N:= 100:
A:= Vector(N):
for k from 1 to N do
f:= combinat:-fibonacci(k);
ds:= [$1..floor(N/k)];
A[k*ds] := A[k*ds] + f*Vector(ds);
od:
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MATHEMATICA
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a[n_] := DivisorSum[n, # * Fibonacci[n/#] &]; Array[a, 38] (* Amiram Eldar, Sep 16 2020 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d*fibonacci(n/d)); \\ Michel Marcus, Sep 16 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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