A085029 Number of prime factors of cyclotomic(n,4), which is A019322(n), the value of the n-th cyclotomic polynomial evaluated at x=4. 1
1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 2, 2, 1, 2, 2, 2, 1, 3, 2, 3, 2, 4, 3, 3, 1, 5, 2, 2, 2, 3, 3, 4, 2, 4, 3, 3, 1, 4, 2, 4, 2, 3, 4, 5, 2, 2, 4, 6, 2, 5, 2, 6, 2, 4, 2, 5, 1, 2, 4, 3, 2, 4, 2, 4, 3, 3, 2, 5, 2, 5, 4, 3, 3, 4, 5, 4, 2, 7, 4, 7, 2, 2, 4, 3, 3, 4, 3, 6, 1, 3, 3, 5, 1, 6, 3, 5, 4 (list; graph; refs; listen; history; text; internal format)
The Mobius transform of this sequence yields A057957, number of prime factors of 4^n-1.
See references at A085021
Table of n, a(n) for n=1..100.
Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 4]]][[2]], {n, 1, 100}]
T. D. Noe, Jun 19 2003