A085028 Number of prime factors of cyclotomic(n,3), which is A019321(n), the value of the n-th cyclotomic polynomial evaluated at x=3.

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, 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, 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

Offset: 1

Author

T. D. Noe, Jun 19 2003

Keywords

• nonn

Comments

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

References

• See references at A085021

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690

Crossrefs

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).

Cf. A019321, A057958, A059885, A143663, A218356, A074477.

Programs

Mathematica

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