A293651 -id:A293651 - cp's OEIS frontend

A293648 Sum of two (possibly negative) coprime cubes in at least 2 ways, but not the sum of 2 noncoprime cubes.

91, 217, 721, 1027, 1729, 3367, 4706, 4921, 4977, 7657, 8587, 8911, 9919, 10621, 14911, 15561, 16263, 20683, 21014, 23877, 25669, 27937, 28063, 31519, 35929, 39331, 40033, 49959, 63693, 68705, 68857, 68913, 73017, 77653, 77779, 97309, 98623, 106597, 109573

Offset: 1

Rosalie Fay, Oct 16 2017

nonn

Not every term is cubefree; some are sb^3 where s is in A159843 and b > 1.

			63693 = 34^3 + 29^3 = 53^3 - 44^3 and 34 & 29 are coprime, as are 53 & -44, but it is not also the sum of cubes of 2 noncoprime integers, so 63693 is in the sequence.

Rosalie Fay, Table of n, a(n) for n = 1..325

Cf. A293647 (allows noncoprime); A293649 (only positives); A293646, A293651

A293646 Sum of two (possibly negative) coprime cubes, but not the sum of 2 non-coprime cubes.

Original entry on oeis.org

1, 2, 7, 9, 19, 26, 28, 35, 37, 61, 63, 65, 91, 98, 117, 124, 126, 127, 133, 169, 215, 217, 218, 271, 279, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 468, 469, 485, 511, 539, 547, 559, 602, 604, 631, 637, 657, 665, 721, 730, 737, 793, 817, 819

Offset: 1

Rosalie Fay, Oct 16 2017

nonn

Not every term is cubefree; some are sb^3 where s is in A159843 and b > 1.

			344 = 7^3 + 1^3 and 344 is not also the sum of cubes of 2 non-coprime integers, so 344 is in the sequence.
152 = 6^3 + (-4)^3 and 6 and -4 are not coprime, so 152 is not in the sequence.

Rosalie Fay, Table of n, a(n) for n = 1..101 (corrected by Ray Chandler, Jan 19 2019)

Cf. A020895 (cubefree); A293645 (allows non-coprime); A293648, A293651

s[n_] := CoprimeQ @@@ ({x, y} /. Solve[n == x^3 + y^3, {x, y}, Integers]);
Reap[For[k = 1, k < 2000, k++, If[Union[s[k]] == {True}, Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Feb 02 2023 *)

A293650 Sum of two (possibly negative) cubes in at least 3 ways (primitive solutions).

Original entry on oeis.org

728, 3367, 4104, 5859, 46683, 65728, 68913, 101528, 124488, 134379, 152551, 155736, 165464, 168112, 184464, 195841, 205352, 289224, 333944, 342657, 402597, 439101, 622232, 625177, 684019, 754299, 757701, 842751, 845208, 1009736, 1016496, 1062936, 1073375

Offset: 1

Rosalie Fay, Oct 16 2017

nonn

Primitive means that the 6 summands are coprime. Not every term is the sum of two coprime cubes. a(1) = A047696(3).

			4104 = 18^3 - 12^3 = 16^3 + 2^3 = 15^3 + 9^3, and 18, -12, 16, 2, 15, 9 are coprime, so 4104 is in the sequence.

Rosalie Fay, Table of n, a(n) for n = 1..664

Cf. A051383 (all solutions); A003825 (positive cubes); A293651 (only coprime); A293645, A293647

cp's OEIS Frontend

A293648 Sum of two (possibly negative) coprime cubes in at least 2 ways, but not the sum of 2 noncoprime cubes.

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A293646 Sum of two (possibly negative) coprime cubes, but not the sum of 2 non-coprime cubes.

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A293650 Sum of two (possibly negative) cubes in at least 3 ways (primitive solutions).

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