A267702 Numbers that are the sum of 3 nonzero squares (A000408) and the sum of 2 positive cubes (A003325).

9, 35, 54, 65, 72, 91, 126, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 370, 432, 468, 513, 539, 576, 637, 686, 728, 730, 737, 756, 793, 854, 945, 1001, 1027, 1064, 1072, 1125, 1216, 1241, 1332, 1339, 1358, 1395, 1456, 1458, 1512, 1547, 1674, 1729, 1736, 1755, 1843, 1853

Offset: 1

Author

Altug Alkan, Jan 23 2016

Keywords

• nonn

Comments

Intersection of A000408 and A003325.

Sequence focuses on the solutions of equation x^3 + y^3 = a^2 + b^2 + c^2 where x, y, a, b, c > 0.

Examples

			9 is a term because 9 = 1^3 + 2^3 = 1^2 + 2^2 + 2^2.
35 is a term because 35 = 2^3 + 3^3 = 1^2 + 3^2 + 5^2.
54 is a term because 54 = 3^3 + 3^3 = 3^2 + 3^2 + 6^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3649

Crossrefs

Cf. A000408, A003325.

Programs

Maple

N:= 1000: # to get all terms <= N
S3:= {seq(seq(seq(a^2+b^2+c^2, c = b .. floor(sqrt(N-a^2-b^2))),
b=a .. floor(sqrt((N-a^2)/2))), a = 1 .. floor(sqrt(N/3)))}:
C2:= {seq(seq(a^3+b^3, b = a .. floor((N-a^3)^(1/3))),a = 1 .. floor((N/2)^(1/3)))}:
sort(convert(S3 intersect C2, list)); # Robert Israel, Jan 25 2016

PARI

isA000408(n) = {my(a, b); a=1; while(a^2+1A003325(n)=#select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=3, 1e4, if(isA000408(n) && isA003325(n), print1(n, ", ")));