A228499 Sums of two rational cubes, excluding cubes and twice cubes.

6, 7, 9, 12, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 34, 35, 37, 42, 43, 48, 49, 50, 51, 53, 56, 58, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 75, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 94, 96, 97, 98, 103, 104, 105, 106, 107, 110, 114, 115, 117, 120, 123, 124

Offset

1,1

Comments

Each term can be written as sum of two rational cubes infinitely many times.

These are all the integers A>0 such that the rank of the elliptic curve x^3 + y^3 = A is positive (A060838(A)>0). - Michael Somos, Feb 29 2020

References

Wacław Sierpiński, Teoria liczb, cz. II, PWN, Warsaw, 1959, pp. 472-473.

Links

Table of n, a(n) for n=1..64.

Index entries for sequences related to sums of cubes

Prog

(PARI) for(n=1, 124, if(ellanalyticrank(ellinit([0, (4*n)^2]))[1]>0, print1(n, ", ")));

Crossrefs

Subsequence of A020897, and hence of A159843.

Cf. A020898, A060838.

Sequence in context: A094698 A361419 A096405 * A309961 A108595 A186079

Adjacent sequences: A228496 A228497 A228498 * A228500 A228501 A228502

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 23 2013

Status

approved