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Search: id:A117342
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| 1, 2, 3, 4, 12, 54, 55, 58, 74, 192, 475, 10188
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OFFSET
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1,2
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COMMENT
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A114536.
Sequence in context: A037397 A053350 A165302 this_sequence A123215 A126129 A102947
Adjacent sequences: A117339 A117340 A117341 this_sequence A117343 A117344 A117345
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KEYWORD
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hard,nonn
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AUTHOR
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Felipe Garcia (fgarciah(AT)ucla.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 09 2006
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EXTENSIONS
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Possibly continues with A114536(464)=11712 & A114536(690)=12840.
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