A064144 a(n) is the number of divisors of n!+1.

2, 2, 2, 3, 3, 4, 3, 4, 8, 4, 2, 6, 4, 4, 8, 32, 8, 64, 4, 4, 8, 8, 12, 4, 4, 4, 2, 4, 8, 32, 16, 16, 32, 4, 32, 64, 2, 4, 16, 128, 2, 8, 16, 8, 8, 8, 16, 4, 32, 32, 64, 16, 16, 4, 4, 16, 8, 16, 4, 16, 16, 8, 32, 8

Offset: 1

Author

Vladeta Jovovic, Sep 11 2001

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..139
• William Gerst, A conjecture on the prime factorization of n!+1, arXiv:1809.07360 [math.GM], 2018.
• Hisanori Mishima, Factorizations of many number sequences

Crossrefs

Cf. A000005, A002583, A027423, A002981, A002982, A064145, A078778, A181764.

Programs

Mathematica

Do[ Print[ DivisorSigma[0, n! + 1]], {n, 1, 40} ]

PARI

a(n) = numdiv(n! + 1); \\ Harry J. Smith, Sep 09 2009

Python

from math import factorial
from sympy import divisor_count
def A064144(n): return divisor_count(factorial(n)+1) # Chai Wah Wu, Oct 20 2023

Formula

a(n) = tau(n!+1).

Extensions

More terms from Robert G. Wilson v, Oct 04 2001

a(42)-a(64) from Harry J. Smith, Sep 09 2009

Edited by Jon E. Schoenfield, Jun 21 2018