OFFSET
1,8
COMMENTS
The cyclotomic polynomial Phi[pqr] can only have coefficients with absolute value > 1 if p,q,r are distinct odd primes, that's why we require 2 < p < q < r. If any of these inequalities is replaced by equality, then Phi[pqr] necessarily has only zero or unit (+-1) coefficients. Sequence A159908 counts all possibilities including these trivial cases.
LINKS
Robin Visser, Table of n, a(n) for n = 1..130
Phil Carmody, "Cyclotomic polynomial puzzles", in: "primenumbers" group, May 9, 2009.
Phil Carmody, David Broadhurst, Maximilian Hasler, Makoto Kamada, Cyclotomic polynomial puzzles, digest of 43 messages in primenumbers Yahoo group, May 9, 2009 - May 23, 2013.
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
EXAMPLE
a(5)=1 is the first nonzero term, since the smallest example for Phi(pqr) having no coefficient > 1 (in abs. value) for odd primes p<q<r is obtained for r=prime(5), namely Phi(3*7*11).
PROG
(PARI) A159909(n) = sum( i=2, n-1, my(pq=prime(n)*prime(i)); sum( j=2, i-1, vecmax(abs(Vec(polcyclo(prime(j)*pq))))==1 ))
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
M. F. Hasler, May 09 2009
EXTENSIONS
Extended by T. D. Noe, May 11 2009
More terms from Robin Visser, Aug 09 2023
STATUS
approved