A300165 Numbers m such that m^2 + 1 can be expressed in more than one way as j^2 + k^2 with j > k > 1 and gcd(j,k) = 1.

47, 72, 73, 83, 98, 112, 122, 123, 128, 132, 133, 138, 142, 148, 157, 162, 172, 173, 174, 177, 183, 187, 191, 192, 200, 203, 208, 212, 213, 216, 217, 228, 233, 237, 242, 252, 253, 255, 265, 268, 273, 278, 288, 293, 294, 302, 307, 313, 317, 319

Offset: 1

Author

Hugo Pfoertner, Feb 27 2018

Keywords

• nonn

Comments

The sequence differs from A299707 by the gcd condition, which excludes representations like 18^2 + 1 = 15^2 + 10^2, 32^2 + 1 = 25^2 + 20^2, 38^2 + 1 = 34^2 + 17^2.

Examples

			a(1) = 47 because its 3 representations satisfy the conditions j > k > 1 and gcd(j,k) = 1: 47^2 + 1 = 2210 = 43^2 + 19^2 = 41^2 + 23^2 = 37^2 + 29^2.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050796, A299707, A300166, A300167, A300168.