A085034 Number of prime factors of cyclotomic(n,9), which is A019327(n), the value of the n-th cyclotomic polynomial evaluated at x=9.

3, 2, 2, 2, 3, 1, 2, 3, 3, 2, 4, 1, 2, 2, 3, 2, 5, 1, 4, 1, 4, 2, 3, 3, 4, 2, 5, 2, 6, 1, 5, 2, 3, 2, 3, 1, 5, 2, 8, 2, 5, 2, 3, 3, 5, 2, 7, 2, 7, 4, 5, 2, 5, 1, 5, 3, 6, 2, 4, 3, 4, 3, 5, 2, 4, 1, 5, 3, 7, 3, 6, 2, 6, 3, 7, 4, 4, 2

Offset: 1

Author

T. D. Noe, Jun 19 2003

Keywords

• nonn

Comments

The Mobius transform of this sequence yields A057952, number of prime factors of 9^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), A085028 (x=3), A085029 (x=4), A085030 (x=5), A085031 (x=6), A085032 (x=7), A085033 (x=8), this sequence (x=9), A085035 (x=10).

Cf. A019327, A057952, A059891, A274909.

Programs

Mathematica

Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 9]]][[2]], {n, 1, 100}]