A277857 Numbers that are the sum of 2 squares with a unique partition and also the sum of 3 nonnegative cubes with a unique partition.

1, 2, 8, 9, 10, 16, 17, 29, 36, 64, 72, 73, 80, 81, 128, 136, 153, 160, 197, 218, 232, 244, 277, 281, 288, 314, 349, 397, 405, 433, 466, 468, 512, 514, 521, 557, 576, 577, 584, 586, 593, 637, 640, 648, 701, 738, 757, 794, 801, 853, 857, 881, 882, 953, 980, 1024, 1028, 1088, 1152, 1217, 1224, 1249, 1268, 1280, 1332, 1341, 1396

Offset: 1

Author

Ilya Gutkovskiy, Nov 02 2016

Keywords

• nonn

Comments

Primes in this sequence are 2, 17, 29, 73, 197, 277, 281, 349, 397, 433, 521, 557, 577, 593, 701, 757, 853, 857, 881, 953, ... (subsequence of A002313).

Examples

			a(1) = 1 because 1 = 0^2 + 1^2 and 1 = 0^3 + 0^3 + 1^3;
a(2) = 2 because 2 = 1^2 + 1^2 and 2 = 0^3 + 1^3 + 1^3;
a(3) = 8 because 8 = 2^2 + 2^2 and 8 = 0^3 + 0^3 + 2^3;
a(4) = 9 because 9 = 0^2 + 3^2 and 9 = 0^3 + 1^3 + 2^3;
a(5) = 10 because 10 = 1^2 + 3^2 and 10 = 1^3 + 1^3 + 2^3, etc.
		

Links

• Index entries for sequences related to sums of squares
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A001481, A002313, A003072, A004825, A125022.

Programs

Mathematica

Select[Range[1400], Length[PowersRepresentations[#1, 2, 2]] == 1 && Length[PowersRepresentations[#1, 3, 3]] == 1 & ]