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

1,3

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A000005, A000045.

Sequence in context: A072056 A356831 A066012 * A064129 A005137 A222959

Adjacent sequences: A063372 A063373 A063374 * A063376 A063377 A063378

Keyword

nonn

Author

Jason Earls, Jul 23 2001

Status

approved