A139691 Discriminants of the normalized general quintic polynomials with nonnegative coefficients.
0, 12, 40, 48, 49, 69, 84, 92, 93, 117, 124, 125, 128, 132, 144, 161, 176, 184, 189, 217, 229, 240, 245, 256, 257, 272, 312, 320, 324, 332, 333, 340, 348, 392, 400, 432, 448, 456, 472, 512, 549, 588, 592, 605, 609, 688, 697, 708, 725, 761, 804, 832, 836, 837
Offset: 1
Keywords
References
- Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
Programs
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Mathematica
aa = {}; a = 1; Do[Print[f]; Do[Do[Do[Do[k = b^2 c^2 d^2 e^2 - 4 a c^3 d^2 e^2 - 4 b^3 d^3 e^2 + 18 a b c d^3 e^2 - 27 a^2 d^4 e^2 - 4 b^2 c^3 e^3 + 16 a c^4 e^3 + 18 b^3 c d e^3 - 80 a b c^2 d e^3 - 6 a b^2 d^2 e^3 + 144 a^2 c d^2 e^3 - 27 b^4 e^4 + 144 a b^2 c e^4 - 128 a^2 c^2 e^4 - 192 a^2 b d e^4 + 256 a^3 e^5 - 4 b^2 c^2 d^3 f + 16 a c^3 d^3 f + 16 b^3 d^4 f - 72 a b c d^4 f + 108 a^2 d^5 f + 18 b^2 c^3 d e f - 72 a c^4 d e f - 80 b^3 c d^2 e f + 356 a b c^2 d^2 e f + 24 a b^2 d^3 e f - 630 a^2 c d^3 e f - 6 b^3 c^2 e^2 f + 24 a b c^3 e^2 f + 144 b^4 d e^2 f - 746 a b^2 c d e^2 f + 560 a^2 c^2 d e^2 f + 1020 a^2 b d^2 e^2 f - 36 a b^3 e^3 f + 160 a^2 b c e^3 f - 1600 a^3 d e^3 f - 27 b^2 c^4 f^2 + 108 a c^5 f^2 + 144 b^3 c^2 d f^2 - 630 a b c^3 d f^2 - 128 b^4 d^2 f^2 + 560 a b^2 c d^2 f^2 + 825 a^2 c^2 d^2 f^2 - 900 a^2 b d^3 f^2 - 192 b^4 c e f^2 + 1020 a b^2 c^2 e f^2 - 900 a^2 c^3 e f^2 + 160 a b^3 d e f^2 - 2050 a^2 b c d e f^2 + 2250 a^3 d^2 e f^2 - 50 a^2 b^2 e^2 f^2 + 2000 a^3 c e^2 f^2 + 256 b^5 f^3 - 1600 a b^3 c f^3 + 2250 a^2 b c^2 f^3 + 2000 a^2 b^2 d f^3 - 3750 a^3 c d f^3 - 2500 a^3 b e f^3 + 3 125 a^4 f^4; If[k > 0 && k < 1000, AppendTo[aa, k]], {b, 0, 30}], {c, 0, 30}], {d, 0, 30}], {e, 0, 30}], {f, 0, 30}]; Union[aa] (*Artur Jasinski*)
Comments