A278567 Maximal coefficient (in absolute value) of cyclotomic polynomial C(N,x), where N = n-th number which is a product of exactly three distinct primes = A007304(n).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2

Offset

1,7

Comments

E. Lehmer (1936) shows that this sequence is unbounded.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Emma Lehmer, On the magnitude of the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 42 (1936), 389-392.

Example

The first 2 occurs in the famous C(105,x), which is x^48+x^47+x^46-x^43-x^42-2*x^41-x^40-x^39+x^36+x^35+x^34+x^33+x^32+x^31-x^28-x^26-x^24-x^22-x^20+x^17+x^16+x^15+x^14+x^13+x^12-x^9-x^8-2*x^7-x^6-x^5+x^2+x+1.

Maple

with(numtheory):
b:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, b(n-1)) while
      bigomega(k)<>3 or nops(factorset(k))<>3 do od; k
    end:
a:= n-> max(map(abs, [coeffs(cyclotomic(b(n), x))])):
seq(a(n), n=1..120);  # Alois P. Heinz, Nov 26 2016

Mathematica

f[n_] := Max[ Abs[ CoefficientList[ Cyclotomic[n, x], x]]]; t = Take[ Sort@ Flatten@ Table[Prime@i Prime@j Prime@k, {i, 3, 35}, {j, 2, i -1}, {k, j -1}], 105]; f@# & /@ t (* Robert G. Wilson v, Dec 09 2016 *)

Crossrefs

See A278571 for smallest m such that a(m) = n.

Cf. A007304, A013595, A160340, A262404, A262405.

See A278570 for another version.

Sequence in context: A303824 A106751 A325469 * A043279 A050433 A031263

Adjacent sequences: A278564 A278565 A278566 * A278568 A278569 A278570

Keyword

nonn

Author

N. J. A. Sloane, Nov 26 2016

Status

approved