A193292 Number of odd divisors of Fibonacci(n).

1, 1, 1, 2, 2, 1, 2, 4, 2, 4, 2, 3, 2, 4, 4, 8, 2, 4, 4, 16, 4, 4, 2, 12, 6, 4, 8, 16, 2, 16, 4, 16, 4, 4, 8, 32, 8, 8, 4, 64, 4, 16, 2, 32, 16, 8, 2, 48, 8, 48, 4, 16, 4, 32, 16, 96, 16, 8, 4, 192, 4, 8, 16, 64, 8, 16, 8, 32, 16, 128, 4, 256, 4, 16, 24, 32

Offset: 1

Author

Michel Lagneau, Jul 21 2011

Keywords

• nonn

Examples

			a(16) = 8 because Fibonacci(16) = 987 = 3 * 7 * 47 and the 8 odd divisors are {1, 3, 7, 21, 47, 141, 329, 987}.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A193291.

Programs

Mathematica

f[n_] := Block[{d = Divisors[Fibonacci[n]]}, Count[OddQ[d], True]]; Table[
  f[n], {n, 110}]

PARI

a(n)=n=fibonacci(n);numdiv(n>>valuation(n,2)) \\ Charles R Greathouse IV, Jul 30 2011

Formula

a(n) = A001227(A000045(n)). - Michel Marcus, Jan 14 2014