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Number of prime factors of cyclotomic(n,10), which is A019328(n), the value of the n-th cyclotomic polynomial evaluated at x=10.
13

%I #19 May 06 2022 13:10:10

%S 2,1,2,1,2,2,2,2,2,1,2,1,3,1,2,2,2,2,1,2,3,4,1,1,3,2,3,3,5,3,3,5,2,3,

%T 3,1,3,1,1,2,4,4,4,3,2,4,2,1,2,3,4,2,4,2,4,2,3,2,2,3,7,1,5,4,2,2,3,3,

%U 3,2,2,3,3,3,3,2,4,5,6,2,6,2,3,2,3,3,3

%N Number of prime factors of cyclotomic(n,10), which is A019328(n), the value of the n-th cyclotomic polynomial evaluated at x=10.

%C The Mobius transform of this sequence yields A057951, number of prime factors of 10^n-1.

%D See references at A085021.

%H Max Alekseyev, <a href="/A085035/b085035.txt">Table of n, a(n) for n = 1..352</a> (first 322 terms from Ray Chandler)

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/phin10.htm">Factorizations of Phi_n(10)</a>

%F a(n) = A001222(A019328(n)). - _Ray Chandler_, May 10 2017

%t Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 10]]][[2]], {n, 1, 100}]

%Y omega(Phi(n,x)): A085021 (x=2), A085028 (x=3), A085029 (x=4), A085030 (x=5), A085031 (x=6), A085032 (x=7), A085033 (x=8), A085034 (x=9), this sequence (x=10).

%Y Cf. A001222, A003060, A005422, A007138, A019328, A057951, A070528, A059892.

%K nonn

%O 1,1

%A _T. D. Noe_, Jun 19 2003