|
%I #15 Aug 12 2023 04:37:52
%S 900,4900,10404,79524,81796,417316,532900,846400,1542564,2464900,
%T 3232804,3334276,3496900,12432676,43850884,50836900,51811204,71470116,
%U 107453956,236975236,253892356,432889636,544102276,864948100,1192597156,1450543396
%N Square numbers whose sum of proper square divisors is also square greater than 1.
%H Amiram Eldar, <a href="/A232557/b232557.txt">Table of n, a(n) for n = 1..1000</a>
%e 10404 = 102^2 is a square number. Sum of proper square divisor of 10404 is 2601 + 1156 + 289 + 36 + 9 + 4 + 1 = 4096 = 64^2.
%t 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]];
%t Select[Range[40000]^2, sqQ[A035316[#] - #]&] (* _Amiram Eldar_, Aug 12 2023 *)
%o (PARI) {for(n=1,10^5,m=n*n;k=sumdiv(m,d,d*issquare(d)*(d<m));if(issquare(k)&&k>>1,print(m)))}
%Y Subsequence of A232556.
%Y Cf. A035316, A232554, A232555.
%K nonn
%O 1,1
%A _Antonio Roldán_, Nov 26 2013
|
