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A054992
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Number of prime divisors of 2^n + 1 (counted with multiplicity).
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18
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1, 1, 2, 1, 2, 2, 2, 1, 4, 3, 2, 2, 2, 3, 4, 1, 2, 4, 2, 2, 4, 3, 2, 3, 4, 4, 6, 2, 3, 6, 2, 2, 5, 4, 5, 4, 3, 4, 4, 2, 3, 6, 2, 3, 7, 5, 3, 3, 3, 7, 6, 3, 3, 6, 6, 3, 5, 3, 4, 4, 2, 5, 7, 2, 6, 6, 3, 4, 5, 7, 3, 5, 3, 5, 7, 4, 6, 10, 2, 3, 10, 5, 6, 5, 4, 5, 5, 4, 4, 11, 6, 2, 5, 4, 5, 3, 5, 6, 9, 6, 2, 9, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The length of row n in A001269.
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
S. S. Wagstaff, Jr., The Cunningham Project
S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.
Mersennewiki, C+(2,n) tables.
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FORMULA
| a(n) = A046051(2n) - A046051(n) - T. D. Noe (noe(AT)sspectra.com), Jun 18 2003
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EXAMPLE
| a(3)=2 because 2^3 + 1 = 9 = 3*3.
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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}]]
A054992[n_Integer] := PrimeOmega[2^n + 1]; Table[A054992[n], {n, 200}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
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CROSSREFS
| Cf. A002586, A002587, A003260, A001269, A001348, A054988, A054989, A054990, A054991, A057934-A057941, A000978.
Cf. A046051 (number of prime factors of 2^n-1).
Cf. A086257 (number of primitive prime factors)
Sequence in context: A104640 A193335 A016727 * A096495 A011776 A098965
Adjacent sequences: A054989 A054990 A054991 * A054993 A054994 A054995
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KEYWORD
| nonn
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AUTHOR
| Arne Ring (arne.ring(AT)epost.de), May 30 2000
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EXTENSIONS
| Extended by Patrick De Geest (pdg(AT)worldofnumbers.com), 10/2000.
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