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%I #18 May 06 2022 13:16:09
%S 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,
%T 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,
%U 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
%N Number of prime factors of cyclotomic(n,2), which is A019320(n), the value of the n-th cyclotomic polynomial evaluated at x=2.
%C The Mobius transform of this sequence yields A046051, the number of prime factors of Mersenne number 2^n-1.
%C The number of prime factors in the primitive part of 2^n-1. - _T. D. Noe_, Jul 19 2008
%H Max Alekseyev, <a href="/A085021/b085021.txt">Table of n, a(n) for n = 1..1206</a> (first 500 term from T. D. Noe)
%H H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/cn/">Factorization of Cyclotomic Numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MobiusTransform.html">Mobius Transform</a>
%e a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89.
%t Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]]
%o (PARI) a(n) = #factor(polcyclo(n, 2))~; \\ _Michel Marcus_, Mar 06 2015
%Y 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).
%Y Cf. A005420, A019320, A046051, A046801, A059499, A064078, A112927, A212953.
%K nonn
%O 1,11
%A _T. D. Noe_, Jun 19 2003
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