A232557 Square numbers whose sum of proper square divisors is also square greater than 1.

900, 4900, 10404, 79524, 81796, 417316, 532900, 846400, 1542564, 2464900, 3232804, 3334276, 3496900, 12432676, 43850884, 50836900, 51811204, 71470116, 107453956, 236975236, 253892356, 432889636, 544102276, 864948100, 1192597156, 1450543396

Offset

1,1

Links

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

Example

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.

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[40000]^2, sqQ[A035316[#] - #]&] (* Amiram Eldar, Aug 12 2023 *)

Prog

(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)))}

Crossrefs

Subsequence of A232556.

Cf. A035316, A232554, A232555.

Sequence in context: A246887 A232556 A069096 * A119541 A173486 A258155

Adjacent sequences: A232554 A232555 A232556 * A232558 A232559 A232560

Keyword

nonn

Author

Antonio Roldán, Nov 26 2013

Status

approved