A103156 -id:A103156 - cp's OEIS frontend

A293691 Numbers z such that x^2 + y^6 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.

17, 365, 745, 1025, 1753, 7813, 8177, 11665, 15641, 16649, 27289, 58825, 59189, 65537, 66265, 66637, 81161, 117665, 118673, 129313, 183185, 250001, 250729, 265721, 273533, 324545, 367649, 531457, 532465, 596977, 746497, 762121, 781441, 864145, 885781, 886145

Offset: 1

XU Pingya, Oct 14 2017

nonn

Subsequence of A293690.

			15^2 + 2^6 = 17^2 and gcd(15, 2, 17) = 1, 17 is a term.
885416^2 + 33^6 = 886145^2 and gcd(885416, 33, 886145) = 1, 886145 is a term.

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

Cf. A103156, A174115, A293690.

z={};Do[If[IntegerQ[(n^2 - y^6)^(1/2)] && GCD[y,n]==1,AppendTo[z,n]],{n,8.9*10^5},{y,(n^2 - 1)^(1/6)}];z

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

Original entry on oeis.org

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

XU Pingya, Oct 14 2017

nonn

Subsequence of A293692.

			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.

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

Cf. A103156, A174115, A293284, A293692.

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

cp's OEIS Frontend

A293691 Numbers z such that x^2 + y^6 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.

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