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A228499 Sums of two rational cubes, excluding cubes and twice cubes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A020898, A060838. Subsequence of A159843.

Sequence in context: A095908 A094698 A096405 * A309961 A108595 A186079

Adjacent sequences:  A228496 A228497 A228498 * A228500 A228501 A228502

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Aug 23 2013

STATUS

approved

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Last modified March 7 19:49 EST 2021. Contains 341931 sequences. (Running on oeis4.)