A232554 Square numbers whose sum of square divisors is also square.

1, 1764, 60516, 82369, 529984, 2056356, 2798929, 3534400, 18181696, 38900169, 96020401, 97121025, 335988900, 455907904, 457318225, 617820736, 1334513961, 1599200100, 2176689025, 3279852900, 4464244225, 8586616896, 15688815025, 24514164900, 33366502225

Offset: 1

Author

Antonio Roldán, Nov 26 2013

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

f[p_, e_] := (p^(2*(1 + Floor[e/2])) - 1)/(p^2 - 1); A035316[1] = 1; A035316[n_] := Times @@ f @@@ FactorInteger[n];
Select[Range[200000]^2, IntegerQ[Sqrt[A035316[#]]]&] (* Amiram Eldar, Aug 12 2023 *)
ssdQ[n_]:=IntegerQ[Sqrt[Total[Select[Divisors[n],IntegerQ[Sqrt[#]]&]]]]; Select[Range[200000]^2,ssdQ] (* Harvey P. Dale, Feb 03 2025 *)

PARI

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

Formula

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