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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. 11
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

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

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

Cf. A019320, A046051.

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 October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)