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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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12
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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
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OFFSET
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1,11
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COMMENTS
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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
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EXAMPLE
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a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89.
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MATHEMATICA
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Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]]
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PROG
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(PARI) a(n) = #factor(polcyclo(n, 2))~; \\ Michel Marcus, Mar 06 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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