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A085021
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Number of prime factors of cyclotomic(n,2), which is A019320(n), the value of the n-th cyclotomic polynomial evaluated at x=2.
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10
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0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 1, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 3, 2, 3, 2, 2, 3, 1, 1, 3, 1, 3, 2, 2, 2, 1, 1, 2, 2, 1, 1, 3, 4, 1, 2, 3, 2, 2, 1, 3, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,11
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COMMENTS
| The Mobius transform of this sequence yields A046051, the number of prime factors of Mersenne number 2^n-1.
The number of prime factors in the primitive part of 2^n-1. - T. D. Noe, Jul 19 2008
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..500
H. Mishima, Factorization of Cyclotomic Numbers
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
Eric Weisstein's World of Mathematics, Mobius Transform
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EXAMPLE
| a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89.
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MATHEMATICA
| Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]]
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CROSSREFS
| Cf. A019320, A046051.
Sequence in context: A078572 A122750 A030421 * A060209 A037830 A174353
Adjacent sequences: A085018 A085019 A085020 * A085022 A085023 A085024
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jun 19 2003
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