A064144 - OEIS

%I #21 Oct 21 2023 01:48:28

%S 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,

%T 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,

%U 16,4,16,16,8,32,8

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

%H Max Alekseyev, <a href="/A064144/b064144.txt">Table of n, a(n) for n = 1..139</a>

%H William Gerst, <a href="https://arxiv.org/abs/1809.07360">A conjecture on the prime factorization of n!+1</a>, arXiv:1809.07360 [math.GM], 2018.

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha104.htm">Factorizations of many number sequences</a>

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

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

%o (PARI) a(n) = numdiv(n! + 1); \\ _Harry J. Smith_, Sep 09 2009

%o (Python)

%o from math import factorial

%o from sympy import divisor_count

%o def A064144(n): return divisor_count(factorial(n)+1) # _Chai Wah Wu_, Oct 20 2023

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

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Sep 11 2001

%E More terms from _Robert G. Wilson v_, Oct 04 2001

%E a(42)-a(64) from _Harry J. Smith_, Sep 09 2009

%E Edited by _Jon E. Schoenfield_, Jun 21 2018