A108046 - OEIS

%I #16 May 25 2017 04:20:53

%S 0,1,1,3,3,7,8,16,22,38,55,98,144,242,381,626,987,1625,2584,4221,6774,

%T 11002,17711,28768,46371,75170,121415,196662,317811,514650,832040,

%U 1346895,2178365,3525566,5702898,9229181,14930352,24160402,39088314

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

%H Indranil Ghosh, <a href="/A108046/b108046.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{k>=1} Fibonacci(k-1)*x^k/(1 - x^k). - _Ilya Gutkovskiy_, May 23 2017

%e 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.

%p 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);

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

%o (PARI) a(n)=if(n<1,1,sumdiv(n,d,fibonacci(d-1))); /* _Joerg Arndt_, Aug 14 2012 */

%o (Python)

%o from sympy import fibonacci, divisors

%o def a(n): return 1 if n<1 else sum([fibonacci(d - 1) for d in divisors(n)]) # _Indranil Ghosh_, May 23 2017

%Y Cf. A000045, A007435.

%K nonn

%O 1,4

%A _Emeric Deutsch_, Jun 01 2005