A273843 Numbers that are the average of 3 nonzero squares and the average of 2 positive cubes.

1, 8, 14, 27, 36, 63, 64, 76, 112, 140, 172, 185, 216, 234, 260, 288, 343, 364, 378, 427, 504, 512, 536, 608, 666, 679, 728, 729, 868, 896, 972, 1000, 1030, 1099, 1112, 1120, 1161, 1270, 1331, 1376, 1404, 1463, 1480, 1628, 1688, 1728, 1750, 1764, 1859, 2052, 2080, 2156

Offset: 1

Author

Altug Alkan, Jun 01 2016

Keywords

• nonn
• easy

Comments

Values of (x^3 + y^3)/2 such that (x^3 + y^3)/2 = (a^2 + b^2 + c^2)/3 where x, y, a, b, c > 0, is soluble.

Examples

			14 is a term because 14 = (1^3 + 3^3)/2 = (1^2 + 4^2 + 5^2)/3.
		

Crossrefs

Cf. A000408, A003325, A267702.

Programs

Mathematica

repQ[n_,k_,e_] := {} != Quiet@ IntegerPartitions[n, {k}, Range[n^ (1/e) ]^e, 1]; Select[Range@ 2156, repQ[2*#,2,3] && repQ[3*#,3,2] &] (* Giovanni Resta, Jun 03 2016 *)

PARI

isA000408(n) = my(a, b) ; a=1 ; while(a^2+1A003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(2*n) && isA000408(3*n), print1(n, ", ")));