A323272 Numbers of the form p_1*p_2*p_3*...*p_r where r is 2 or an odd number > 2, and the p_i are distinct primes congruent to 1 mod 4 such that Legendre(p_i/p_j) = -1 for all i != j.

65, 85, 185, 265, 365, 481, 485, 493, 533, 565, 629, 685, 697, 785, 865, 949, 965, 985, 1037, 1073, 1157, 1165, 1189, 1241, 1261, 1285, 1385, 1417, 1465, 1565, 1585, 1649, 1685, 1765, 1769, 1781, 1853, 1865, 1921, 1937, 1985, 2117, 2165, 2173

Offset: 1

Author

N. J. A. Sloane, Jan 11 2019

Keywords

• nonn

Comments

If k is a term, the Pell equation x^2 - k*y^2 = -1 has a solution [Dirichlet, Newman (1977)]. This is only a sufficient condition, there are many other solutions, see A031396.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Morris Newman, A note on an equation related to the Pell equation, The American Mathematical Monthly 84.5 (1977): 365-366.

Crossrefs

Cf. A002144, A031396. Includes the union of A322781 and A323271.