A227029 Primitive solutions c to Diophantine equation a^2 + b^3 = c^5, with a, b, c > 0.

8, 19, 24, 28, 32, 36, 75, 81, 88, 96, 136, 176, 224, 225, 250, 328, 369, 395, 432, 468, 500, 512, 537, 648, 701, 710, 864, 980, 1000, 1078, 1089, 1125, 1216, 1225, 1296, 1440, 1536, 1620, 1734, 1764, 1792, 1800, 1944, 2000, 2028, 2048, 2178, 2304, 2528, 2628

Offset

1,1

Comments

Terms in A178130 not equal to (some previous term)*k^6, k>1.

Some c have more than one solutions for (a,b): 432, 1944, 3249, 3528, 5184, 7220, 10000. For example, 432^5 = 3732480^2 + 10368^3 = 3359232^2 + 15552^3, 3528^5 = 714208320^2 + 331632^3 = 464679936^2 + 691488^3 (are there 3 or more solutions?).

First two primes are a(2) = 19, a(25) = 701.

Links

Zak Seidov, Table of n, a(n) for n = 1..111 (all terms up to 20000)

Example

8^5 = 104^2 + 28^3.

Crossrefs

Cf. A178130.

Sequence in context: A290185 A274397 A178130 * A260004 A144171 A017485

Adjacent sequences: A227026 A227027 A227028 * A227030 A227031 A227032

Keyword

nonn

Author

Zak Seidov, Jun 28 2013

Status

approved