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.

43175, 1382000, 10495575, 44230400, 134984375, 335890800, 726002375, 1415475200, 2550752775, 4319750000, 6957037175, 10749024000, 16039143575, 23233036400, 32803734375, 45296844800, 61335734375, 81626713200, 106964218775, 138236000000, 176428301175

Offset

1,1

Comments

The squarefree part is always 5.

Links

Table of n, a(n) for n=1..21.

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.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

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

Adjacent sequences: A134447 A134448 A134449 * A134451 A134452 A134453

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