A136032 Number of prime factors (with multiplicity) of 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

Offset

1,1

Comments

If the conjecture that all Mersenne composites are squarefree is true, then this sequence is identical to A135975. - Felix Fröhlich, Aug 24 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..183

Formula

a(n) = A001222(A065341(n)). - Michel Marcus, Aug 24 2014

Mathematica

a = {}; Do[If[PrimeQ[n] && !PrimeQ[2^n - 1], w = 2^n - 1; c = FactorInteger[w]; d = Length[c]; b = 0; Do[b = b + c[[k]][[2]], {k, 1, d}]; AppendTo[a, b]], {n, 2, 150}]; a
PrimeOmega/@Select[2^Prime[Range[100]]-1, !PrimeQ[#]&] (* Harvey P. Dale, Nov 01 2016 *)

Prog

(PARI) forprime(p=2, 1e3, if(!ispseudoprime(2^p-1), print1(bigomega(2^p-1), ", "))) \\ Felix Fröhlich, Aug 24 2014

Crossrefs

Cf. A001222, A065341, A135975.

Sequence in context: A074595 A372754 A084126 * A135975 A334796 A140361

Adjacent sequences: A136029 A136030 A136031 * A136033 A136034 A136035

Keyword

nonn

Author

Artur Jasinski, Dec 11 2007

Extensions

More terms from Michel Marcus, Nov 04 2013

Definition adjusted by Felix Fröhlich, Aug 24 2014

More terms from Felix Fröhlich, Aug 24 2014

Status

approved