A108046 Inverse Moebius transform of Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, ...

0, 1, 1, 3, 3, 7, 8, 16, 22, 38, 55, 98, 144, 242, 381, 626, 987, 1625, 2584, 4221, 6774, 11002, 17711, 28768, 46371, 75170, 121415, 196662, 317811, 514650, 832040, 1346895, 2178365, 3525566, 5702898, 9229181, 14930352, 24160402, 39088314

Offset

1,4

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Formula

G.f.: Sum_{k>=1} Fibonacci(k-1)*x^k/(1 - x^k). - Ilya Gutkovskiy, May 23 2017

Example

a(4)=3 because the divisors of 4 are 1,2,4 and the first, second and fourth Fibonacci numbers are 0, 1 and 2, respectively, having sum 3.

Maple

with(combinat): with(numtheory): f:=n->fibonacci(n-1): g:=proc(n) local div: div:=divisors(n): sum(f(div[j]), j=1..tau(n)) end: seq(g(n), n=1..45);

Mathematica

a[n_] := DivisorSum[n, Fibonacci[#-1]&]; Array[a, 40] (* Jean-François Alcover, Dec 17 2015 *)

Prog

(PARI) a(n)=if(n<1, 1, sumdiv(n, d, fibonacci(d-1))); /* Joerg Arndt, Aug 14 2012 */
(Python)
from sympy import fibonacci, divisors
def a(n): return 1 if n<1 else sum([fibonacci(d - 1) for d in divisors(n)]) # Indranil Ghosh, May 23 2017

Crossrefs

Cf. A000045, A007435.

Sequence in context: A320294 A304179 A182559 * A286110 A116157 A056357

Adjacent sequences: A108043 A108044 A108045 * A108047 A108048 A108049

Keyword

nonn

Author

Emeric Deutsch, Jun 01 2005

Status

approved