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 A238097 Number of monic cubic polynomials with coefficients from {1..n} and maximum coefficient equal to n, for which all three roots are integers. 4
 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 3, 2, 1, 2, 3, 1, 3, 0, 3, 3, 1, 1, 4, 3, 1, 1, 3, 2, 3, 1, 2, 3, 2, 0, 4, 5, 2, 2, 2, 1, 3, 3, 3, 3, 1, 0, 5, 4, 1, 2, 4, 4, 3, 1, 2, 2, 3, 1, 5, 6, 1, 2, 3, 2, 3, 1, 4, 6, 2, 0, 5, 5, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 REFERENCES D. Andrica and E. J. Ionascu, On the number of polynomials with coefficients in [n], An. St. Univ. Ovidius Constanta, 2013, to appear. LINKS Zak Seidov, Table of n, a(n) for n = 1..1000 EXAMPLE a(11) = 2 with polynomials x^3 + 6*x^2 + 11*x + 6 = (x+1) * (x+2) * (x+3) and x^3 + 7*x^2 + 11*x + 5 = (x+1)^2 * (x+5). - Michael Somos, Feb 23 2014 MATHEMATICA Table[p = Flatten[Table[{a, b, c, 1}, {a, n}, {b, n}, {c, n}], 2]; cnt = 0; Do[If[Max[p[[i]]] == n, poly = p[[i]].x^Range[0, 3]; r = Rest[FactorList[poly]]; If[Total[Transpose[r][[2]]] == 3 && Union[Coefficient[Transpose[r][[1]], x]] == {1}, Print[{n, r}]; cnt++]], {i, Length[p]}]; cnt, {n, 20}] (* T. D. Noe, Feb 22 2014 *) PROG (PARI) {a(n) = if( n<1, 0, sum(a1=1, n, sum(a2=1, n, sum(a3=1, n, vecmax([a1, a2, a3]) == n && vecsum( factor( Pol([1, a1, a2, a3]))[, 2]) == 3))))}; /* Michael Somos, Feb 23 2014 */ CROSSREFS Cf. A006218, A066955, A238096, A238098. Sequence in context: A133831 A325613 A305054 * A066955 A089048 A329443 Adjacent sequences: A238094 A238095 A238096 * A238098 A238099 A238100 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 22 2014 EXTENSIONS Definition corrected by Giovanni Resta, Feb 22 2014 Extended by T. D. Noe, Feb 22 2014 STATUS approved

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Last modified February 2 12:48 EST 2023. Contains 360021 sequences. (Running on oeis4.)