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A117343
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Position of n in A114536.
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0
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1, 6, 12, 20, 35, 48, 56, 72, 99, 108, 143, 30, 208, 200, 320, 272, 323, 144, 437, 110, 567
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OFFSET
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1,2
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COMMENTS
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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.
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, ..., . - Robert G. Wilson v, Mar 09 2006
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LINKS
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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]; Table[ Position[t, n, 1, 1], {n, 18}] // Flatten
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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