

A228499


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


1



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
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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. 472473.


LINKS



PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



