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 A085021 Number of prime factors of cyclotomic(n,2), which is A019320(n), the value of the n-th cyclotomic polynomial evaluated at x=2. 12
 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; text; internal format)
 OFFSET 1,11 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 LINKS Max Alekseyev, Table of n, a(n) for n = 1..1206 (first 500 term from T. D. Noe) H. Mishima, Factorization of Cyclotomic Numbers Eric Weisstein's World of Mathematics, Cyclotomic Polynomial Eric Weisstein's World of Mathematics, Mobius Transform EXAMPLE a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89. MATHEMATICA Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]] PROG (PARI) a(n) = #factor(polcyclo(n, 2))~; \\ Michel Marcus, Mar 06 2015 CROSSREFS omega(Phi(n,x)): this sequence (x=2), A085028 (x=3), A085029 (x=4), A085030 (x=5), A085031 (x=6), A085032 (x=7), A085033 (x=8), A085034 (x=9), A085035 (x=10). Cf. A005420, A019320, A046051, A046801, A059499, A064078, A112927, A212953. Sequence in context: A329041 A238744 A030421 * A060209 A037830 A174353 Adjacent sequences: A085018 A085019 A085020 * A085022 A085023 A085024 KEYWORD nonn AUTHOR T. D. Noe, Jun 19 2003 STATUS approved

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Last modified December 6 15:25 EST 2023. Contains 367610 sequences. (Running on oeis4.)