A277857 - OEIS

%I #9 Nov 27 2016 21:44:10

%S 1,2,8,9,10,16,17,29,36,64,72,73,80,81,128,136,153,160,197,218,232,

%T 244,277,281,288,314,349,397,405,433,466,468,512,514,521,557,576,577,

%U 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

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

%C 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).

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%e a(1) = 1 because 1 = 0^2 + 1^2 and 1 = 0^3 + 0^3 + 1^3;

%e a(2) = 2 because 2 = 1^2 + 1^2 and 2 = 0^3 + 1^3 + 1^3;

%e a(3) = 8 because 8 = 2^2 + 2^2 and 8 = 0^3 + 0^3 + 2^3;

%e a(4) = 9 because 9 = 0^2 + 3^2 and 9 = 0^3 + 1^3 + 2^3;

%e a(5) = 10 because 10 = 1^2 + 3^2 and 10 = 1^3 + 1^3 + 2^3, etc.

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

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

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Nov 02 2016