A181186 - OEIS

%I #45 Jul 29 2023 06:49:24

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

%T 5,2,4,2,4,1,4,4,3,3,1,3,4,5,3,4,4,5,2,2,2,6,4,2,5,3,7,4,3,2,5,3,4,4,

%U 4,2,7,6,7,3,5,2,4,3,8,8,6,4

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

%C a(101) >= 3. See link to factordb.com. - _Hugo Pfoertner_, Aug 07 2019

%H Yurii Ivanov, <a href="/A181186/b181186.txt">Table of n, a(n) for n = 1..103</a> (terms 1..100 from Sean A. Irvine and Hugo Pfoertner, term 101 from Tyler Busby)

%H Sean A. Irvine, <a href="/A181186/a181186.txt">Factorizations of (2^n-1)*n!+1</a>

%H factordb.com, <a href="http://factordb.com/index.php?query=%282%5En-1%29*n%21%2B1&amp;use=n&amp;n=100&amp;VP=on&amp;VC=on&amp;EV=on&amp;OD=on&amp;PR=on&amp;FF=on&amp;PRP=on&amp;CF=on&amp;U=on&amp;C=on&amp;perpage=20&amp;format=1&amp;sent=Show">Status of (2^n-1)*n!+1</a>.

%F a(n) = A001222(A052589(n)+1). - _Michel Marcus_, Apr 08 2023

%t Table[PrimeOmega[(2^n-1)n!+1],{n,90}] (* The program takes a long time to run. *) (* _Harvey P. Dale_, Feb 10 2019 *)

%Y Cf. A001222, A052589.

%K nonn

%O 1,4

%A _Jason Earls_, Oct 09 2010

%E More terms from _Sean A. Irvine_, Sep 15 2012