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
Robert Israel, Table of n, a(n) for n = 1..4740
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 17 2002
STATUS
approved