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Square numbers whose sum of square divisors is also square.
4

%I #17 Aug 12 2023 04:37:42

%S 1,1764,60516,82369,529984,2056356,2798929,3534400,18181696,38900169,

%T 96020401,97121025,335988900,455907904,457318225,617820736,1334513961,

%U 1599200100,2176689025,3279852900,4464244225,8586616896,15688815025,24514164900,33366502225

%N Square numbers whose sum of square divisors is also square.

%H Amiram Eldar, <a href="/A232554/b232554.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A046655(n)^2.

%e 60516 = 246^2. Sum of square divisors: 60516 + 15129 + 6724 + 1681 + 36 + 9 + 4 + 1 = 84100 = 290^2.

%t f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n];

%t Select[Range[200000]^2, IntegerQ[Sqrt[A035316[#]]]&] (* _Amiram Eldar_, Aug 12 2023 *)

%o (PARI) {for(n=1,10^5,m=n*n;k=sumdiv(m,d,d*issquare(d));if(issquare(k),print(m)))}

%Y Cf. A035316, A046655, A232555, A232556, A232557.

%K nonn

%O 1,2

%A _Antonio Roldán_, Nov 26 2013