cp's OEIS Frontend

A polynomial is called flat iff it is of height 1, where the height is the largest absolute value of the coefficients.

A cyclotomic polynomial phi(n) is said of order 3 iff n=pqr with distinct (usually odd) primes p,q,r.

It is well known that phi(n) is flat if n has less than 3 odd prime factors, so this sequence includes all numbers of the form 2pq, with primes q>p>2, i.e. A075819. Sequence A117223 lists the complement, i.e. odd terms in this sequence, which start with 231 = 3*7*11.

Moreover, Kaplan shows that the present sequence also includes pqr if r = +-1 (mod pq). Sequence A160352 lists the subsequence of all such numbers, while A160354 lists elements which are not of this form.

Kaplan (2007) has shown that this is a subsequence of A117223 (and thus of A160350; see there for the reference), i.e., the cyclotomic polynomial phi(n) has coefficients in {0,1,-1} for indices n listed here.

This is a subsequence of A160352 which drops the requirement that p > 2.

See A160350 for further details and references.

Kaplan (2007) has shown that Phi(pqr) has coefficients in {0,1,-1} if r = +-1 (mod pq), where pA160350 which do not satisfy this equality.

Yet most elements are even, i.e. in A075819. Sequence A160355 is the subsequence of odd terms. See A160350 for more details.