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A046051
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Number of prime factors of Mersenne number M(n) = 2^n - 1 (counted with multiplicity).
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27
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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; internal format)
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OFFSET
| 1,4
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COMMENTS
| Length of row n of A001265.
PrimeOmega(2^n - 1) -- Vladimir Joseph Stephan Orlovsky, Jul 22 2011.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..500 (derived from Brillhart et al.)
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Mersenne Number
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FORMULA
| Mobius transform of A085021 - T. D. Noe (noe(AT)sspectra.com), Jun 19 2003
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EXAMPLE
| a(4) = 2 because 2^4 - 1 = 15 = 3*5.
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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 (zerinvarylajos(AT)yahoo.com), Apr 11 2008
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MATHEMATICA
| a[q_] := Module[{x, n}, x=FactorInteger[2^n-1]; n=Length[x]; Sum[Table[x[i]][2]], {i, n}][j]], {j, n}]]
A046051[n_Integer] := PrimeOmega[2^n - 1]; Table[A046051[n], {n, 200}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
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CROSSREFS
| Cf. A000043, A000668, A001348, A054988, A054989, A054990, A054991, A054992, A057951-A057958.
Cf. A085021.
Sequence in context: A079167 A199570 A032741 * A025812 A109698 A029231
Adjacent sequences: A046048 A046049 A046050 * A046052 A046053 A046054
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com).
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