A168177 - OEIS

%I #26 Jul 07 2024 04:48:16

%S 1,1,1,2,1,4,1,4,2,4,1,5,4,4,4,4,2,7,2,8,4,3,3,7,3,3,5,6,5,7,3,7,5,6,

%T 3,10,5,8,4,8,7,7,9,6,5,5,4,11,5,6,3,6,4,9,6,11,5,2,4,15,2,6,5,8,5,7,

%U 4,5,7,9,2,13,7,5,8,6,4,7,3,11,5,3,3,11,6

%N Number of prime factors of n! + 2^n - 1, counted with multiplicity.

%H Kevin P. Thompson, <a href="/A168177/b168177.txt">Table of n, a(n) for n = 1..106</a>

%H Florian Luca and Igor E. Shparlinski, <a href="https://doi.org/10.5802/jtnb.524">On the largest prime factor of n! + 2^n - 1</a>, Journal de Théorie des Nombres de Bordeaux 17 (2005), 859-870.

%F a(n) = A001222(A127986(n)). - _Amiram Eldar_, Feb 05 2020

%e 6! + 2^6 - 1 = 783 = 3^3 * 29, hence a(6) = 4.

%t PrimeOmega @ Table[n! + 2^n - 1, {n, 1, 30}] (* _Amiram Eldar_, Feb 05 2020 *)

%o (Magma) pfmult := func< n | &+[ d[2]: d in Factorization(n) ] >; [ pfmult(Factorial(n)+2^n-1): n in [1..50] ]; //Some values were computed using Dario Alpern's ECM Factorization Program.

%o (PARI) a(n)=bigomega(n!+2^n-1) \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A001222, A127986 (n!+2^n-1), A139024 (number of distinct prime factors), A139023 (smallest prime factor), A127987 (largest prime factor).

%K nonn

%O 1,4

%A _Klaus Brockhaus_, Nov 20 2009

%E a(76)-a(81) from _Amiram Eldar_, Feb 05 2020

%E a(82) onwards from _Kevin P. Thompson_, Jun 29 2022