OFFSET

1,1

COMMENTS

A representation k = (x^3 + y^3 + z^3)/(x*y*z) is equivalent to 2 representations k = a/b + b/c + c/a, given by a=y^2*z, b=z^2*x, c=x^2*y and a=y*z^2, b=x*y^2, c=z*x^2. - Dean Hickerson, Jul 14 2003

For each a(n) > 5 there are infinitely many representations. - David J. Rusin, Jul 15 2003

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1000

David J. Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Broken link]

David J. Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Cached copy of html wrapper for paper but in pdf format (so none of the links work)]

David J. Rusin, For which values of n is a/b + b/c + c/a = n solvable? [Cached copy of .txt file]

EXAMPLE

15 is in the sequence because 15 = (7^3 + (-3)^3 + (-1)^3)/(7*-3*-1) = (7^3 - 3^3 - 1^3)/(7*3*1) = (343 - 27 - 1)/21. This is equivalent to 15 = -9/7 - 7/147 + 147/9 or 15 = -3/63 - 63/49 + 49/3.

16 = (70^3 + (-31)^3 + (-9)^3)/(70*-31*-9) = (70^3 - 31^3 - 9^3)/(70*31*9) = (343000 - 29791 - 729)/19530.

PROG

(PARI) is(k) = abs(k-4)==1 || ellanalyticrank(ellinit([0, k^2, 0, -72*k, -16*(4*k^3+27)]))[1]; \\ Jinyuan Wang, Jul 27 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jul 18 2003

EXTENSIONS

More terms from David J. Rusin, Jul 26 2003

STATUS

approved