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A066769
a(n) = Sum_{d|n} d*Fibonacci(n/d).
1
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
OFFSET
1,2
COMMENTS
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
REFERENCES
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, pp. 29 ff.
LINKS
FORMULA
G.f.: Sum_{i>0} i*x^i/(1-x^i-x^(2*i)). - Vladeta Jovovic, Oct 06 2003
MAPLE
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:
convert(A, list); # Robert Israel, Feb 08 2016
MATHEMATICA
a[n_] := DivisorSum[n, # * Fibonacci[n/#] &]; Array[a, 38] (* Amiram Eldar, Sep 16 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*fibonacci(n/d)); \\ Michel Marcus, Sep 16 2020
CROSSREFS
Sequence in context: A236309 A304588 A335058 * A323765 A270780 A304251
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 17 2002
STATUS
approved