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%I #19 Aug 12 2023 04:37:46
%S 3528,5292,8820,10584,12348,17640,19404,22932,24696,26460,29988,33516,
%T 37044,38808,40572,45864,51156,52920,54684,58212,59976,61740,65268,
%U 67032,68796,72324,74088,75852,81144,82908,89964,93492,97020,100548,102312,104076,107604
%N Nonsquare numbers whose sum of proper square divisors is a square greater than 1.
%H Amiram Eldar, <a href="/A232555/b232555.txt">Table of n, a(n) for n = 1..10000</a>
%e 8820 is nonsquare number. Sum of proper square divisor: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2.
%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], !IntegerQ[Sqrt[#]] && sqQ[A035316[#]] &] (* _Amiram Eldar_, Aug 12 2023 *)
%o (PARI) {for(n=1,10^5,if(issquare(n)==0,k=sumdiv(n,d,d*issquare(d)); if(issquare(k)&&k>>1, print(n))))}
%Y Subsequence of A232556.
%Y Cf. A232554, A232557.
%K nonn
%O 1,1
%A _Antonio Roldán_, Nov 26 2013
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