A087073 Mobius transform of A051664, the number of nonzero terms in the n-th cyclotomic polynomial.

2, 0, 1, 0, 3, 0, 5, 0, 0, 0, 9, 0, 11, 0, 1, 0, 15, 0, 17, 0, 1, 0, 21, 0, 0, 0, 0, 0, 27, 0, 29, 0, 3, 0, 7, 0, 35, 0, 3, 0, 39, 0, 41, 0, 0, 0, 45, 0, 0, 0, 5, 0, 51, 0, 3, 0, 5, 0, 57, 0, 59, 0, 0, 0, 15, 0, 65, 0, 7, 0, 69, 0, 71, 0, 0, 0, 15, 0, 77, 0, 0, 0, 81, 0, 21, 0, 9, 0, 87, 0, 5, 0, 9, 0, 9

Offset: 1

Author

T. D. Noe, Aug 08 2003

Keywords

• nonn

Comments

Note that a(n) = 0 for even n and a(n) = n-2 for prime n. It appears that the following are true: a(1) is the only positive even term, all odd numbers eventually appear in the sequence, a(n) = 0 if n is squareful and a(n) > 0 if n is squarefree. Assuming the truth of the last statement, we can show that if distinct odd primes p and q divide n, then A051664(n) > p + q - 2.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A051664.

Formula

a(n) = Sum{d|n} mu(n/d) A051664(d)

Extensions

Definition corrected: "inverse moebius transform" to "moebius transform" by Wouter Meeussen, Jan 17 2009