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A320662
Numbers k for which there are numbers 0 < m <= k such that k^3 + m^3 is a square.
0
2, 8, 18, 21, 26, 32, 37, 46, 50, 65, 70, 72, 84, 88, 91, 98, 104, 105, 112, 128, 148, 162, 184, 189, 190, 200, 234, 242, 249, 260, 273, 280, 288, 312, 330, 333, 336, 338, 345, 352, 354, 364, 371, 392, 407, 414, 416, 420
OFFSET
1,1
COMMENTS
The sequence is infinite since if u is in the sequence then so is u*t^2, t, u >= 1. - Marius A. Burtea and David A. Corneth, Oct 23 2018
EXAMPLE
8^3 + 4^3 = 512 + 64 = 576 = 24^2, so 8 is part of the sequence.
18^3 + 9^3 = 5832 + 729 = 6561 = 81^2, so 18 is part of the sequence.
91^3 + 65^3 = 753571 + 274625 = 1028196 = 1014^2, so 91 is part of the sequence.
7^3 + 0^3 = 343 + 0 = 343, 7^3 + 1^3 = 343 + 1 = 344, 7^3 + 2^3 = 343 + 8 = 351,7^3 + 4^3 = 343 + 64 = 407, 7^3 + 5^3 = 343 + 125 = 468, 7^3 + 6^3 = 343 + 216 = 559 and 7^3 + 7^3 = 343 + 343 = 686. Numbers 343, 344, 351, 407, 468, 559 and 686 are not squares, so 7 is not part of the sequence.
MATHEMATICA
Select[Range@ 420, AnyTrue[Range[#1]^3 + #2, IntegerQ@ Sqrt@ # &] & @@ {#, #^3} &] (* Michael De Vlieger, Nov 05 2018 *)
PROG
(PARI) is(n) = for(m=1, n, if(issquare(n^3+m^3), return(1))); 0 \\ Felix Fröhlich, Oct 22 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Oct 18 2018
STATUS
approved