A202057 - OEIS

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

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OFFSET

1,1

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

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A004613, A201278, A072437.

Sequence in context: A000415 A172000 A096691 * A263651 A070216 A100829

Adjacent sequences: A202054 A202055 A202056 * A202058 A202059 A202060

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 10 2011

STATUS

approved