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A046051 Number of prime factors of Mersenne number M(n) = 2^n - 1 (counted with multiplicity). 30
0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 2, 5, 1, 3, 3, 4, 1, 6, 1, 6, 4, 4, 2, 7, 3, 3, 3, 6, 3, 7, 1, 5, 4, 3, 4, 10, 2, 3, 4, 8, 2, 8, 3, 7, 6, 4, 3, 10, 2, 7, 5, 7, 3, 9, 6, 8, 4, 6, 2, 13, 1, 3, 7, 7, 3, 9, 2, 7, 4, 9, 3, 14, 3, 5, 7, 7, 4, 8, 3, 10, 6, 5, 2, 14, 3, 5, 6, 10, 1, 13, 5, 9, 3, 6, 5, 13, 2, 5, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Length of row n of A001265.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..500 (derived from Brillhart et al.)

R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Mersenne Number

FORMULA

Mobius transform of A085021. - T. D. Noe, Jun 19 2003

EXAMPLE

a(4) = 2 because 2^4 - 1 = 15 = 3*5.

MAPLE

with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(stirling2(n, 2)) fi end: seq(a(n), n=2..100); # Zerinvary Lajos, Apr 11 2008

MATHEMATICA

a[q_] := Module[{x, n}, x=FactorInteger[2^n-1]; n=Length[x]; Sum[Table[x[i]][2]], {i, n}][j]], {j, n}]]

a[n_Integer] := PrimeOmega[2^n - 1]; Table[a[n], {n, 200}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

PROG

(PARI) a(n)=bigomega(2^n-1) \\ Charles R Greathouse IV, Apr 01 2013

CROSSREFS

Cf. A000043, A000668, A001348, A054988, A054989, A054990, A054991, A054992, A057951-A057958, A085021.

Sequence in context: A199570 A239707 A032741 * A025812 A263001 A109698

Adjacent sequences:  A046048 A046049 A046050 * A046052 A046053 A046054

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.