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
Keywords
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
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))))}