A007436 Moebius transform of Fibonacci numbers.

1, 0, 1, 2, 4, 6, 12, 18, 32, 50, 88, 134, 232, 364, 604, 966, 1596, 2544, 4180, 6708, 10932, 17622, 28656, 46206, 75020, 121160, 196384, 317432, 514228, 831374, 1346268, 2177322, 3524488, 5701290, 9227448, 14927632, 24157816, 39083988

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

After a(4) = 2, there are no primes in this sequence. Every element thereafter has at least two prime factors, the semiprimes (intersection of A007436 and A001358) starting 4, 6, 134, 831374, ... - Jonathan Vos Post, Dec 15 2004

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..500
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A001358.

Programs

Mathematica

mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*Fibonacci /@ d)]; Table[ mt[n], {n, 38}] (* Robert G. Wilson v Dec 10 2004 *)
a[n_] := DivisorSum[n, Fibonacci[#] MoebiusMu[n/#]&]; Array[a, 40] (* Jean-François Alcover, Dec 01 2015 *)

PARI

a(n)=sumdiv(n,d,fibonacci(d)*moebius(n/d))

Formula

Row sums of the triangle generated by A054525 * A127647. - Gary W. Adamson, Jan 22 2007

G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/(1 - x - x^2). - Ilya Gutkovskiy, Apr 25 2017

Extensions

More terms from Robert G. Wilson v, Dec 10 2004