1,2

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.

a(23)=216, a(24)<=768, a(25)<=725, a(26)<=832, a(27)<=783, a(28)=182, a(29)<=899, a(30)<=972, a(31)<=992, a(32)=70, a(34)=288, a(35)=675, a(36)=154, a(37)<=784, a(38)<=1000, a(40)=306, a(41)=435, a(44)=506, a(45)<=1225, a(49)<=800, a(52)<=1378, a(54)=60, a(55)=84, a(56)=418, a(57)=195, a(58)=90, a(59)<=861, a(60)=126, ..., . - (rgwv(AT)rgwv.com), Mar 09 2006

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]; Table[ Position[t, n, 1, 1], {n, 18}] // Flatten

Cf. A114536.

Sequence in context: A056930 A064971 A130199 this_sequence A028611 A141808 A144187

Adjacent sequences: A117340 A117341 A117342 this_sequence A117344 A117345 A117346

hard,nonn

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

a(19)-a(21) from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 02 2006