

A306104


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


3



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
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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: A090221 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



