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

1,1

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.

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A372754 A084126 A136032 * A334796 A140361 A237769

Adjacent sequences: A135972 A135973 A135974 * A135976 A135977 A135978

Keyword

nonn

Author

Artur Jasinski, Dec 09 2007

Extensions

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

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

Status

approved