[seqfan] Help! Integers of the form x^3 + 2y^3 (x, y > 0) exactly in 4 ways.

[zak seidov]

Dear seqfans,

Is this list of any credit?

Not sure that there are no gaps (suspiciously all terms are multiples of 3456125 = 5^3*43*643 ?!)


Can anyone check/fill/extend this?

What about more (5,6,...) ways?

Thanks,
Zak

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Integers expressible in the form x^3 + 2y^3 (x, y > 0) exactly in 4 ways.
575012796875, 4600102375000, 15525345515625, 36800819000000, 71876599609375, 88726937046875, 124202764125000, 197229389328125, 294406552000000, 419184328921875, 575012796875000, 709815496375000, 765342032640625, 944764425675125, 993622113000000, 1263303114734375, 1577835114625000, 1940668189453125, 2355252416000000, 2825037871046875, 3353474631375000, 3944012773765625, 4600102375000000, 5325193511859375, 6122736261125000, 6996180699578125, 7948976904000000, 8984574951171875, 10106424917875000, 11317976880890625, 12622680917000000, 14023987102984375
575012796875:  {x, y} = {8195, 2310}, {7225, 4625}, {6413, 5379}, {275, 6600};
4600102375000:  {x, y} = {16390, 4620}, {14450, 9250}, {12826, 10758}, {550, 13200}.