

A306103


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Numbers n such that A100073(n) >= 3; 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

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


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A100073, A058957, A056924.
Subsequence of A306102. Contains A306104 as a subsequence.
Sequence in context: A291788 A291787 A257410 * A045566 A274368 A214572
Adjacent sequences: A306100 A306101 A306102 * A306104 A306105 A306106


KEYWORD

nonn


AUTHOR

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


STATUS

approved



