A293693 Numbers z such that x^2 + y^7 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.

33, 1094, 2219, 4097, 6283, 39063, 40156, 69985, 78157, 82221, 148109, 411772, 412865, 450834, 524289, 526475, 602413, 823575, 827639, 893527, 1347831, 2391485, 2430547, 2500001, 2502187, 2803256, 3323543, 4783001, 4787065, 5307257, 7282969, 8957953, 9036077

Offset: 1

Author

XU Pingya, Oct 14 2017

Keywords

• nonn

Comments

Subsequence of A293692.

Examples

			31^2 + 2^7 = 33^2 and gcd(31, 2, 33) = 1, 33 is a term.
8879827^2 + 60^7 = 9036077^2 and gcd(8879827, 60, 9036077) = 1, 9036077 is a term.
		

Links

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

Crossrefs

Cf. A103156, A174115, A293284, A293692.

Programs

Mathematica

z={};Do[If[IntegerQ[(n^2 - y^7)^(1/2)] && GCD[y,n]==1,AppendTo[z,n]],{n,9.7*10^6},{y,(n^2 - 1)^(1/7)}];z