A232555 Nonsquare numbers whose sum of proper square divisors is a square greater than 1.

3528, 5292, 8820, 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, 81144, 82908, 89964, 93492, 97020, 100548, 102312, 104076, 107604

Offset: 1

Author

Antonio Roldán, Nov 26 2013

Keywords

• nonn

Examples

			8820 is nonsquare number. Sum of proper square divisor: 1764 + 441 + 196 + 49 + 36 + 9 + 4 + 1 = 2500 = 50^2.
		

Links

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

Crossrefs

Subsequence of A232556.

Cf. A232554, 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]; sqQ[n_] := n>1 && IntegerQ[Sqrt[n]];
Select[Range[100000], !IntegerQ[Sqrt[#]] && sqQ[A035316[#]] &] (* Amiram Eldar, Aug 12 2023 *)

PARI

{for(n=1,10^5,if(issquare(n)==0,k=sumdiv(n,d,d*issquare(d)); if(issquare(k)&&k>>1, print(n))))}