A085031 Number of prime factors of cyclotomic(n,6), which is A019324(n), the value of the n-th cyclotomic polynomial evaluated at x=6.

1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 4, 1, 2, 2, 1, 1, 4, 1, 3, 3, 2, 2, 1, 1, 2, 3, 2, 2, 3, 3, 5, 2, 2, 2, 2, 1, 4, 3, 3, 2, 3, 2, 3, 1, 3, 3, 3, 2, 2, 4, 3, 3, 3, 4, 3, 1, 4, 3, 4, 3, 2, 2, 2, 5, 1, 3, 4, 3, 3, 2, 2, 4, 3, 3, 2, 3, 7, 2, 3, 1, 4, 2, 3, 1, 2

Offset: 1

Author

T. D. Noe, Jun 19 2003

Keywords

• nonn

Comments

The Mobius transform of this sequence yields A057955, number of prime factors of 6^n-1.

References

• See references at A085021

Links

• Max Alekseyev, Table of n, a(n) for n = 1..430

Crossrefs

omega(Phi(n,x)): A085021 (x=2), A085028 (x=3), A085029 (x=4), A085030 (x=5), this sequence (x=6), A085032 (x=7), A085033 (x=8), A085034 (x=9), A085035 (x=10).

Cf. A019324, A057955, A059888, A274907.

Programs

Mathematica

Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 6]]][[2]], {n, 1, 100}]