OFFSET
1,2
COMMENTS
This differs from A013594.
For squarefree k, are there an infinite number of cyclotomic polynomials Phi(k,x) of height n? This is true for n=1 because it is known that there are an infinite number of flat cyclotomic polynomials with k the product of three distinct primes. See A117223. - T. D. Noe, Apr 22 2008
There are an infinite number of cyclotomic polynomials of height n if the following generalization of Kaplan's theorem 2 is true: Let N be the product of distinct odd primes and let p be one of those primes. Let q any prime such that q = p (mod N/p), then the height of Phi(Nq/p,x) is the same as the height of Phi(N,x). By Dirichlet's theorem, there are an infinite number of primes q. [From T. D. Noe, Apr 13 2010]
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118-126.
MATHEMATICA
f[n_] := f[n] = Max@ Abs@ CoefficientList[ Cyclotomic[n, x], x]; Do[ f@n, {n, 100000}]; t = Array[f, 31000]; Table[ Position[t, n, 1, 1], {n, 25}]//Flatten
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 31 2008
EXTENSIONS
More terms from T. D. Noe, Apr 22 2008
STATUS
approved