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A306104 Numbers that are the difference of two positive squares in at least four ways. 3

%I #18 Jan 11 2020 01:55:35

%S 96,105,120,135,144,160,165,168,189,192,195,216,224,225,231,240,255,

%T 264,273,280,285,288,297,312,315,320,336,345,351,352,357,360,375,384,

%U 385,399,400,405,408,416,420,429,432,435,440,441,448,455,456,459,465,480,483,495

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

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

%H Metin Sariyar, <a href="/A306104/b306104.txt">Table of n, a(n) for n = 1..10000</a>

%H Geoffrey Campbell, <a href="https://www.linkedin.com/groups/4510047/4510047-6421706912643014658">Numbers that are the difference of two squares in two or more ways</a>, Number Theory Group on LinkedIn, July 8, 2018.

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

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

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

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

%Y Cf. A100073, A058957, A056924.

%Y Subsequence of A306103, A306102 and A058957.

%K nonn

%O 1,1

%A Geoffrey B. Campbell and _M. F. Hasler_, Jul 10 2018

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Last modified April 19 07:38 EDT 2024. Contains 371782 sequences. (Running on oeis4.)