A117342 Records in A113436.

1, 2, 3, 4, 12, 54, 55, 58, 74, 192, 475, 10188

Offset: 1

Author

Felipe Garcia (fgarciah(AT)ucla.edu) and Robert G. Wilson v, Mar 09 2006

Keywords

• hard
• nonn

Comments

A114536: Let the height of a polynomial be the largest coefficient in absolute value. Then A114536(n) is the maximal height of a divisor of x^n-1 with integral coefficients.

Records occur at A113436(k): 1, 6, 12, 20, 30, 60, 84, 90, 105, 120, 180, 210.

Crossrefs

Cf. A114536.

Programs

Mathematica

cyc[n_] := cyc[n] = Cyclotomic[n, x]; f[n_] := Block[{sd = Take[Subsets@Divisors@n, {2, lmt = 2^(DivisorSigma[0, n] - 1)}], lst = {}, y = x^n - 1}, For[i = 1, i < lmt, i++, pr = Expand[Times @@ (cyc[ # ] & /@ sd[[i]])]; AppendTo[lst, Max@ Abs@ CoefficientList[pr, x]]; AppendTo[lst, Max@ Abs@ CoefficientList[Together[y/pr], x]]]; Max@lst];
t = Array[f, 359]; r = 0; Do[ a = t[[n]]; If[ a > r, Print[{n, a}]; r = a], {n, 359}]

Extensions

Possibly continues with A114536(464)=11712 & A114536(690)=12840.