A085035 Number of prime factors of cyclotomic(n,10), which is A019328(n), the value of the n-th cyclotomic polynomial evaluated at x=10.

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, 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, 3, 2, 2, 3, 3, 3, 3, 2, 4, 5, 6, 2, 6, 2, 3, 2, 3, 3, 3

Offset: 1

Author

T. D. Noe, Jun 19 2003

Keywords

• nonn

Comments

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

References

• See references at A085021.

Links

• Max Alekseyev, Table of n, a(n) for n = 1..352 (first 322 terms from Ray Chandler)
• Makoto Kamada, Factorizations of Phi_n(10)

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), A085034 (x=9), this sequence (x=10).

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

Programs

Mathematica

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

Formula

a(n) = A001222(A019328(n)). - Ray Chandler, May 10 2017