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

Author

Arkadiusz Wesolowski, Aug 23 2013

Keywords

• nonn

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

• Index entries for sequences related to sums of cubes

Crossrefs

Subsequence of A020897, and hence of A159843.

Cf. A020898, A060838.

Programs

PARI

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