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

1,1

Comments

Subsequence of A293690.

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A103156, A174115, A293690.

Sequence in context: A121824 A120287 A222678 * A365678 A002197 A070148

Adjacent sequences: A293688 A293689 A293690 * A293692 A293693 A293694

Keyword

nonn

Author

XU Pingya, Oct 14 2017

Status

approved