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Number of prime factors of cyclotomic(n,3), which is A019321(n), the value of the n-th cyclotomic polynomial evaluated at x=3.
11

%I #13 May 22 2022 19:57:06

%S 1,2,1,2,2,1,1,2,1,1,2,1,1,1,1,3,2,2,2,2,1,2,2,1,2,1,3,2,3,2,3,2,1,3,

%T 2,1,2,2,4,1,3,3,2,2,3,1,4,3,5,2,2,2,3,2,3,2,3,3,2,1,2,2,1,2,3,2,3,2,

%U 2,1,1,1,4,3,3,2,3,4,3,2,3,2,4,2,2,1,3,3,3,2,2,2,2,3,2,2,3,2,2,4

%N Number of prime factors of cyclotomic(n,3), which is A019321(n), the value of the n-th cyclotomic polynomial evaluated at x=3.

%C The Mobius transform of this sequence yields A057958, number of prime factors of 3^n-1.

%D See references at A085021

%H Max Alekseyev, <a href="/A085028/b085028.txt">Table of n, a(n) for n = 1..690</a>

%t Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 3]]][[2]], {n, 1, 100}]

%Y omega(Phi(n,x)): A085021 (x=2), this sequence (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. A019321, A057958, A059885, A143663, A218356, A074477.

%K nonn

%O 1,2

%A _T. D. Noe_, Jun 19 2003