A260549 Primitive values n such that the square with opposite corners (0,0) and (n,n) contains a point (x,y) with integer coordinates, with 0 < x,y < n, at an integer distance from three of the four corners.

52, 195, 700, 740, 867, 996, 1443, 2145, 3364, 6015, 6240, 7800, 8400, 9165, 9375, 10879, 10952, 11184, 11352, 11484, 11492, 11997, 12675, 13156, 14355, 14739, 20280, 20415, 20625, 20988, 21125, 21320, 21853, 22472, 23069, 26180, 26588, 27189, 28168, 30195

Offset: 1

Author

Mark Underwood and Giovanni Resta, Jul 29 2015

Keywords

• nonn

Comments

Primitiveness condition prescribes that, if n is in the sequence because of the interior point (x, y), then GCD(x, y, n) = 1.

Some values admit more than one qualifying interior point. For example, for n = 21125 we have both (4416, 3737) and (8357, 7524).

This sequence is a superset of A215365, which only contains even values.

Examples

			700 is in the sequence because the point (304,297) is at distance 425 from (0,0), 495 from (700,0) and 565 from (700,700) and GCD(700,304,297) = 1.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..75 (terms < 130000)

Crossrefs

Cf. A215365.