A306103 Numbers that are the difference of two positive squares in at least three ways.

45, 48, 63, 72, 75, 80, 96, 99, 105, 112, 117, 120, 128, 135, 144, 147, 153, 160, 165, 168, 171, 175, 176, 180, 189, 192, 195, 200, 207, 208, 216, 224, 225, 231, 240, 243, 245, 252, 255, 256, 261, 264, 272, 273, 275, 279, 280, 285, 288, 297, 300

Offset: 1

Author

Geoffrey B. Campbell and M. F. Hasler, Jul 10 2018

Keywords

• nonn

Comments

Numbers n such that A100073(n) >= 3; see there for more information & formulas.

Examples

			48 = 7^2 - 1^2 = 8^2 - 4^2 = 13^2 - 11^2.
		

Links

• Metin Sariyar, Table of n, a(n) for n = 1..10000
• Geoffrey Campbell, Numbers that are the difference of two squares in two or more ways, Number Theory Group on LinkedIn, July 8, 2018.

Crossrefs

Cf. A100073, A058957, A056924.

Subsequence of A306102. Contains A306104 as a subsequence.

Programs

Mathematica

Select[Range[300], Length[FindInstance[x^2 - y^2 == # && x>y>0, {x,y}, Integers, 3 ]] == 3 &] (* Giovanni Resta, Jul 10 2018 *)

PARI

select( is(n)=A100073(n)>2, [1..300])

Formula

A306103 = { n = 2k+1 | A056924(n) > 2 } U { n = 4k | A056924(n/4) > 2 }.