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A134450 a(n) = square root of the square part of discriminant of Brioschi quintic polynomial x^5-10*n*x^3+45*n^2*x-n^2. 1
43175, 1382000, 10495575, 44230400, 134984375, 335890800, 726002375, 1415475200, 2550752775, 4319750000, 6957037175, 10749024000, 16039143575, 23233036400, 32803734375, 45296844800, 61335734375, 81626713200, 106964218775, 138236000000, 176428301175 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The squarefree part is always 5.
LINKS
Matthew Moore, Theorems and Algorithms Associated with Solving the General Quintic [Appears to give incorrect formula for the Brioschi quintic]
Tito Piezas III and Eric Weisstein's World of Mathematics, Brioschi Quintic Form.
FORMULA
a(n) = 25*n^4*(1728*n-1). - Klaus Brockhaus, Oct 28 2007
G.f.: 25*x*(1729*x^4 + 44938*x^3+114048*x^2+44918*x+1727) / (x-1)^6. - Colin Barker, Sep 02 2013
MATHEMATICA
Table[25n^4(1728n-1), {n, 1, 100}]
PROG
(PARI) a(n) = my(p=poldisc(x^5 - 10*n*x^3 + 45*n^2*x - n^2)); sqrtint(p/core(p)); \\ Michel Marcus, Mar 02 2023
CROSSREFS
Cf. A134448.
Sequence in context: A205733 A205914 A205906 * A141085 A151623 A151660
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 26 2007, Oct 28 2007
EXTENSIONS
Corrected by Klaus Brockhaus, Oct 28 2007
More terms from Colin Barker, Sep 02 2013
Name corrected by Amiram Eldar, Mar 02 2023
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)