A202057 Numbers which are not perfect squares and such that all prime divisors are congruent to 1 or 2 mod 4.

2, 5, 8, 10, 13, 17, 20, 26, 29, 32, 34, 37, 40, 41, 50, 52, 53, 58, 61, 65, 68, 73, 74, 80, 82, 85, 89, 97, 101, 104, 106, 109, 113, 116, 122, 125, 128, 130, 136, 137, 145, 146, 148, 149, 157, 160, 164, 170, 173, 178, 181, 185, 193, 194, 197, 200, 202, 205, 208, 212, 218, 221, 226, 229, 232, 233, 241, 244, 250, 257, 260, 265, 269, 272, 274

Offset: 1

Author

Artur Jasinski, Dec 10 2011

Keywords

• nonn

Comments

This sequence follows conjecture from A201278 that Mordell's elliptic curve x^3-y^2 = d can contain points {x,y} with quadratic extension sqrt(k) over rationals if and only k belongs to this sequence.

Members of A072437 that are not perfect squares. - Franklin T. Adams-Watters, Dec 15 2011

Examples

			a(3)=8 because 8 isn't perfect square and only one prime divisor 2 is congruent to 2 mod 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004613, A201278, A072437.

Programs

Mathematica

aa = {}; Do[pp = FactorInteger[j]; if = False; Do[If[Mod[pp[[n]][[1]], 4] == 3 || Mod[pp[[n]][[1]], 4] == 0, if = True], {n, 1, Length[pp]}]; If[if == False, If[IntegerQ[Sqrt[j]] == False, AppendTo[aa, j]]], {j, 2, 200}]; aa
seqQ[n_] := !IntegerQ@Sqrt[n] && AllTrue[FactorInteger[n][[;; , 1]], MemberQ[{1, 2}, Mod[#, 4]] &]; Select[Range[300], seqQ] (* Amiram Eldar, Mar 21 2020 *)