A117342 - OEIS

%I #4 Mar 30 2012 17:31:18

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

%N Records in A113436.

%C 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.

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

%t 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 t = Array[f, 359]; r = 0; Do[ a = t[[n]]; If[ a > r, Print[{n, a}]; r = a], {n, 359}]

%Y Cf. A114536.

%K hard,nonn

%O 1,2

%A Felipe Garcia (fgarciah(AT)ucla.edu) and _Robert G. Wilson v_, Mar 09 2006

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