

A080642


Cubefree taxicab numbers: the smallest cubefree number that is the sum of 2 cubes in n ways.


2




OFFSET

1,1


COMMENTS

A necessary condition for the sum to be cubefree is that each pair of cubes be relatively prime.
If the sequence is infinite, then the MordellWeil rank of the elliptic curve of rational solutions to x^3 + y^3 = a(n) tends to infinity with n. In fact, the rank exceeds C*log(n) for some constant C>0 (see Silverman p. 339).  Jonathan Sondow, Oct 22 2013


LINKS

Table of n, a(n) for n=1..4.
J. H. Silverman, Taxicabs and Sums of Two Cubes, Amer. Math. Monthly, 100 (1993), 331340.


FORMULA

a(n) >= A011541(n) for n > 0, with equality for n = 1, 2 (only?).  Jonathan Sondow, Oct 25 2013


EXAMPLE

2 = 1^3 + 1^3
1729 = 12^3 + 1^3 = 10^3 + 9^3
15170835645 = 2468^3 + 517^3 = 2456^3 + 709^3 = 2152^3 + 1733^3
1801049058342701083 = 1216500^3 + 92227^3 = 1216102^3 + 136635^3 = 1207602^3 + 341995^3 = 1165884^3 + 600259^3


CROSSREFS

Cf. A011541.
Sequence in context: A129061 A233132 A011541 * A108331 A263076 A162554
Adjacent sequences: A080639 A080640 A080641 * A080643 A080644 A080645


KEYWORD

hard,more,nonn


AUTHOR

Stuart Gascoigne (Stuart.G(AT)scoigne.com), Feb 28 2003


STATUS

approved



