This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080642 #30 Jun 23 2024 05:50:15 %S A080642 2,1729,15170835645,1801049058342701083 %N A080642 Cubefree taxicab numbers: the smallest cubefree number that is the sum of 2 positive cubes in n ways. %C A080642 A necessary condition for the sum to be cubefree is that each pair of cubes be relatively prime. %C A080642 If the sequence is infinite, then the Mordell-Weil 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 %H A080642 Bernd C. Kellner, <a href="https://doi.org/10.5281/zenodo.10963985">On primary Carmichael numbers</a>, Integers 22 (2022), Article #A38, 39 pp.; arXiv:<a href="https://arxiv.org/abs/1902.11283">1902.11283</a> [math.NT], 2019. %H A080642 J. H. Silverman, <a href="https://doi.org/10.1080/00029890.1993.11990409">Taxicabs and Sums of Two Cubes</a>, Amer. Math. Monthly, 100 (1993), 331-340. %F A080642 a(n) >= A011541(n) for n > 0, with equality for n = 1, 2 (only?). - _Jonathan Sondow_, Oct 25 2013 %e A080642 2 = 1^3 + 1^3, %e A080642 1729 = 12^3 + 1^3 = 10^3 + 9^3, %e A080642 15170835645 = 2468^3 + 517^3 = 2456^3 + 709^3 = 2152^3 + 1733^3, %e A080642 1801049058342701083 = 1216500^3 + 92227^3 = 1216102^3 + 136635^3 = 1207602^3 + 341995^3 = 1165884^3 + 600259^3. %Y A080642 Cf. A011541. %K A080642 hard,more,nonn %O A080642 1,1 %A A080642 Stuart Gascoigne (Stuart.G(AT)scoigne.com), Feb 28 2003 %E A080642 Name clarified by _Jeppe Stig Nielsen_, Aug 21 2020