A102708 Composite numbers a(n) having a GCD with Pell_x(a(n))-1 equal to 1 (where Pell_x(n) is the x solution of the Pell-Fermat equation: x^2 - n y^2 = 1). There is no square in the sequence because the Pell-Fermat equation has no solution for them.

27, 51, 65, 85, 123, 125, 145, 171, 185, 187, 243, 265, 267, 291, 325, 339, 363, 365, 387, 411, 425, 445, 451, 459, 481, 485, 493, 531, 533, 565, 603, 627, 629, 685, 697, 699, 731, 771, 779, 785, 803, 843, 845, 865, 867, 901, 925, 949, 963, 965, 985, 1003