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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A237781 A205904 A061627 * A111886 A343989 A343988

Adjacent sequences: A232551 A232552 A232553 * A232555 A232556 A232557

Keyword

nonn

Author

Antonio Roldán, Nov 26 2013

Status

approved