A070745 Numbers z such that the Diophantine equation x^2 + y^3 = z^2 has solutions with x, y > 0.

3, 6, 10, 14, 15, 17, 21, 24, 28, 29, 35, 36, 42, 43, 45, 48, 55, 57, 60, 62, 63, 66, 76, 78, 80, 81, 90, 91, 99, 105, 112, 118, 119, 120, 123, 127, 129, 132, 136, 140, 141, 143, 147, 153, 154, 155, 161, 162, 165, 168, 171, 172, 179, 185, 190, 192, 195, 209, 210

Offset: 1

Author

Benoit Cloitre, May 14 2002

Keywords

• easy
• nonn

Examples

			42 is in the sequence because 6^2 + 12^3 = 42^2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066647.

Programs

Mathematica

q[n_] := Length[Reduce[a^2 + b^3 == n^2 && a > 0 && b > 0, {a, b}, Integers]] > 0; Select[Range[210], q] (* Amiram Eldar, Mar 20 2025 *)

PARI

for(n=0,350,if(sum(i=1,n,sum(j=1,n,if(i^2+j^3-n^2,0,1)))>0,print1(n,",")))

Formula

a(n) = sqrt(A066647(n)). - Amiram Eldar, Mar 20 2025

Extensions

Corrected and edited by John W. Layman, May 21 2002