A087969 - OEIS

A087969

Integers m such that gcd(2^m+1, m^2) is not a square.

9, 45, 50, 63, 81, 99, 117, 150, 153, 171, 207, 225, 261, 279, 315, 333, 350, 369, 387, 405, 423, 441, 450, 477, 495, 531, 549, 550, 567, 585, 603, 605, 639, 650, 657, 693, 711, 729, 747, 765, 801, 819, 850, 855, 873, 891, 909, 927, 950, 963, 981, 1014, 1017

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

For m = 9: gcd(513, 81) = 27 is not a square number, so 9 is a term.

MATHEMATICA

Do[s=Sqrt[GCD[n^2, 2^n+1]]; If[ !IntegerQ[s], Print[n]], {n, 1, 1000}]

PROG

(PARI) isok(m) = !issquare(gcd(2^m+1, m^2)); \\ Michel Marcus, Aug 27 2019

(Magma) [m:m in [1..1020]|not IsSquare(Gcd(1+2^m, m^2))]; // Marius A. Burtea, Aug 27 2019