A066647 -id:A066647 - cp's OEIS frontend

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

Benoit Cloitre, May 14 2002

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

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

Cf. A066647.

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 *)

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,",")))

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

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

A066648 Cubes of the form a^2 + b^3 with a, b > 0.

Original entry on oeis.org

512, 1000, 2744, 21952, 32768, 35937, 64000, 175616, 185193, 274625, 357911, 373248, 405224, 474552, 729000, 1157625, 1404928, 1481544, 2000376, 2097152, 2197000, 2299968, 2744000, 3241792, 3652264, 3723875, 4096000, 5451776, 7189057, 8000000, 10218313, 10360232

Offset: 1

Reinhard Zumkeller, Dec 17 2001

nonn

			8^3 = a(0) = 512 = 169 + 343 = 13^2 + 7^3;
10^3 = a(1) = 1000 = 784 + 216 = 28^2 + 6^3.

Amiram Eldar, Table of n, a(n) for n = 1..5000

Cf. A055394, A066647, A228946.

q[n_] := Length[Reduce[a^2 + b^3 == n && a > 0 && b > 0, {a, b}, Integers]] > 0; Select[Range[220]^3, q] (* Amiram Eldar, Mar 20 2025 *)

a(n) = A228946(n)^3. - R. J. Mathar, Dec 03 2015

cp's OEIS Frontend

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

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