A063375 Number of divisors of Fibonacci(n).

1, 1, 2, 2, 2, 4, 2, 4, 4, 4, 2, 15, 2, 4, 8, 8, 2, 16, 4, 16, 8, 4, 2, 72, 6, 4, 16, 16, 2, 64, 4, 16, 8, 4, 8, 160, 8, 8, 8, 64, 4, 64, 2, 32, 32, 8, 2, 336, 8, 48, 8, 16, 4, 128, 16, 96, 32, 8, 4, 960, 4, 8, 32, 64, 8, 64, 8, 32, 32, 128, 4, 1536, 4, 16, 48, 32, 16, 128, 4, 512, 128, 8

Offset: 1

Author

Jason Earls, Jul 23 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1408 (terms 1..1000 from T. D. Noe using Blair Kelly's data)
• Blair Kelly, Fibonacci and Lucas Factorizations.
• Florian Luca, Arithmetic Functions of Fibonacci Numbers, The Fibonacci Quarterly, Vol. 37, No. 3 (1999), pp. 265-268.

Crossrefs

Cf. A000005, A000045.

Programs

Mathematica

Table[Length[Divisors[Fibonacci[n]]], {n, 120}] (* Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)
Table[DivisorSigma[0, Fibonacci[n]], {n, 1, 100}] (* Vaclav Kotesovec, Feb 13 2019 *)

PARI

j=[]; for(n=1,150,j=concat(j,numdiv(fibonacci(n)))); j

PARI

for (n = 1, 466, write("b063375.txt", n, " ", numdiv(fibonacci(n)))) \\ Harry J. Smith, Aug 20 2009

Formula

a(n) = A000005(A000045(n)). - Omar E. Pol, Dec 20 2008

a(n) >= A000045(A000005(n)), with equality if and only if n = 1, 2 or 4 (Luca, 1999). - Amiram Eldar, Jan 12 2022