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

1,2

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).

Links

Table of n, a(n) for n=1..67.

Index entries for sequences related to sums of squares

Index entries for sequences related to sums of cubes

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A047469 A283774 A037456 * A360427 A369204 A237280

Adjacent sequences: A277854 A277855 A277856 * A277858 A277859 A277860

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2016

Status

approved