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%I #22 Aug 12 2023 04:37:49
%S 900,3528,4900,5292,8820,10404,10584,12348,17640,19404,22932,24696,
%T 26460,29988,33516,37044,38808,40572,45864,51156,52920,54684,58212,
%U 59976,61740,65268,67032,68796,72324,74088,75852,79524,81144,81796,82908,89964,93492
%N Numbers whose sum of proper square divisors is a square greater than 1.
%H Amiram Eldar, <a href="/A232556/b232556.txt">Table of n, a(n) for n = 1..10000</a>
%e Sum of proper square divisors of 5292: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2 is square number.
%t f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n]; sqQ[n_] := n>1 && IntegerQ[Sqrt[n]];
%t Select[Range[100000], sqQ[A035316[#] - If[IntegerQ[Sqrt[#]], #, 0]] &] (* _Amiram Eldar_, Aug 12 2023 *)
%o (PARI) {for(n=1,10^5,k=sumdiv(n,d,d*issquare(d)*(d<n));if(issquare(k)&&k>>1,print(n)))}
%Y Disjoint union of A232555 and A232557.
%Y Cf. A232554.
%K nonn
%O 1,1
%A _Antonio Roldán_, Nov 26 2013
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