A306104 Numbers that are the difference of two positive squares in at least four ways.

96, 105, 120, 135, 144, 160, 165, 168, 189, 192, 195, 216, 224, 225, 231, 240, 255, 264, 273, 280, 285, 288, 297, 312, 315, 320, 336, 345, 351, 352, 357, 360, 375, 384, 385, 399, 400, 405, 408, 416, 420, 429, 432, 435, 440, 441, 448, 455, 456, 459, 465, 480, 483, 495

Offset

1,1

Comments

Numbers n such that A100073(n) >= 4; see there for more information & formulas.

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.

Formula

A306104 = { n = 2k+1 | A056924(n) > 3 } U { n = 4k | A056924(n/4) > 3 }.

Example

96 = 10^2 - 2^2 = 11^2 - 5^2 = 14^2 - 10^2 = 25^2 - 23^2.

Mathematica

Select[Range@495, Length@ FindInstance[x^2 - y^2 == # && x>y>0, {x, y}, Integers, 4] == 4 &] (* Giovanni Resta, Jul 10 2018 *)

Prog

(PARI) select( is(n)=A100073(n)>3, [1..500])

Crossrefs

Cf. A100073, A058957, A056924.

Subsequence of A306103, A306102 and A058957.

Sequence in context: A334654 A045528 A181470 * A257411 A175116 A153484

Adjacent sequences: A306101 A306102 A306103 * A306105 A306106 A306107

Keyword

nonn

Author

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

Status

approved