A232556 Numbers whose sum of proper square divisors is a square greater than 1.

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

Offset: 1

Author

Antonio Roldán, Nov 26 2013

Keywords

• nonn

Examples

			Sum of proper square divisors of 5292: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2 is square number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Disjoint union of A232555 and A232557.

Cf. A232554.

Programs

Mathematica

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 *)

PARI

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