

A085021


Number of prime factors of cyclotomic(n,2), which is A019320(n), the value of the nth cyclotomic polynomial evaluated at x=2.


12



0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 1, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 3, 2, 3, 2, 2, 3, 1, 1, 3, 1, 3, 2, 2, 2, 1, 1, 2, 2, 1, 1, 3, 4, 1, 2, 3, 2, 2, 1, 3, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,11


COMMENTS

The Mobius transform of this sequence yields A046051, the number of prime factors of Mersenne number 2^n1.
The number of prime factors in the primitive part of 2^n1.  T. D. Noe, Jul 19 2008


LINKS



EXAMPLE

a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89.


MATHEMATICA

Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]]


PROG

(PARI) a(n) = #factor(polcyclo(n, 2))~; \\ Michel Marcus, Mar 06 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



