A052589 -id:A052589 - cp's OEIS frontend

A181186 Number of prime factors of (2^n - 1) * n! + 1, counted with multiplicity.

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

Offset: 1

Jason Earls, Oct 09 2010

nonn

a(101) >= 3. See link to factordb.com. - Hugo Pfoertner, Aug 07 2019

Yurii Ivanov, Table of n, a(n) for n = 1..103 (terms 1..100 from Sean A. Irvine and Hugo Pfoertner, term 101 from Tyler Busby)
Sean A. Irvine, Factorizations of (2^n-1)*n!+1
factordb.com, Status of (2^n-1)*n!+1.

Cf. A001222, A052589.

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

a(n) = A001222(A052589(n)+1). - Michel Marcus, Apr 08 2023

More terms from Sean A. Irvine, Sep 15 2012

A052867 E.g.f.: log(-(-1+x)^2/(-1+2*x)).

Original entry on oeis.org

0, 0, 2, 12, 84, 720, 7440, 90720, 1280160, 20563200, 370863360, 7424524800, 163419379200, 3923023104000, 102011054745600, 2856483889459200, 85697132032512000, 2742350070620160000, 93240613775941632000

Offset: 0

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Previous name was: A simple grammar.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 838

spec := [S,{B=Sequence(Z,1 <= card),C=Prod(B,B),S= Cycle(C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Range[0,19]! CoefficientList[Series[Log[-(-1 + x)^2/(-1 + 2 x)], {x, 0, 19}], x] (* Vincenzo Librandi, Jul 09 2015 *)

D-finite with Recurrence: {a(1)=0, a(2)=2, (2*n^2+2*n)*a(n)-3*(n+1)*a(n+1)+a(n+2)}.
a(n) = -2*GAMMA(n+1)+2^(n+1)*GAMMA(n+1).
a(n) = 2*A052589(n-1). - R. J. Mathar, Jun 03 2022

cp's OEIS Frontend

A181186 Number of prime factors of (2^n - 1) * n! + 1, counted with multiplicity.

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