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A232556
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Numbers whose sum of proper square divisors is a square greater than 1.
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4
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900, 3528, 4900, 5292, 8820, 10404, 10584, 12348, 17640, 19404, 22932, 24696, 26460, 29988, 33516, 37044, 38808, 40572, 45864, 51156, 52920, 54684, 58212, 59976, 61740, 65268, 67032, 68796, 72324, 74088, 75852, 79524, 81144, 81796, 82908, 89964, 93492
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OFFSET
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1,1
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LINKS
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EXAMPLE
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Sum of proper square divisors of 5292: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2 is square number.
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MATHEMATICA
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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]];
Select[Range[100000], sqQ[A035316[#] - If[IntegerQ[Sqrt[#]], #, 0]] &] (* Amiram Eldar, Aug 12 2023 *)
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PROG
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(PARI) {for(n=1, 10^5, k=sumdiv(n, d, d*issquare(d)*(d<n)); if(issquare(k)&&k>>1, print(n)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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