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A108046 Inverse Moebius transform of Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, ... 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)