A135975 Number of prime factors (without multiplicity) in Mersenne composites A065341.

2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 4, 5, 2, 4, 3, 4, 5, 3, 2, 2, 3, 6, 2, 4, 4, 6, 2, 5, 3, 4, 2, 2, 3, 2, 3, 2, 5, 3, 4, 4, 3, 5, 2, 3, 3, 6, 5, 2, 2, 5, 3, 9, 4, 3, 5, 2, 8, 4, 4, 3, 5, 2, 4, 6, 3, 4, 2, 7, 3, 4, 4, 2, 5, 4, 5, 3, 5, 4, 3, 6, 4, 3, 4, 3, 4, 4

Offset: 1

Author

Artur Jasinski, Dec 09 2007

Keywords

• nonn

Comments

Currently the smallest prime exponent p for which 2^p-1 is incompletely factored is p = 1213. - Gord Palameta, Aug 06 2018

Links

• Gord Palameta, Table of n, a(n) for n = 1..183
• GIMPS, Status of M1213
• S. S. Wagstaff, Jr., Main Tables from the Cunningham Project: cofactor of M1213 is C297.

Crossrefs

Cf. A000225, A001221, A065341, A054723, A134852.

Programs

Mathematica

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; AppendTo[k, d]], {n, 1, 40}]; k
(PrimeNu /@ Select[2^Prime[Range[40]] - 1, ! PrimeQ[#] &]) (* Jean-François Alcover, Aug 13 2014 *)

PARI

forprime(p=1, 1e3, if(!ispseudoprime(2^p-1), print1(omega(2^p-1), ", "))) \\ Felix Fröhlich, Aug 12 2014

Formula

a(n) = A001221(A065341(n)). - Michel Marcus, Aug 07 2018

Extensions

a(29)-a(46) from Felix Fröhlich, Aug 12 2014

a(47)-a(100) from Gord Palameta, Aug 07 2018