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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Disjoint union of A232555 and A232557.

Cf. A232554.

Sequence in context: A258888 A287800 A246887 * A069096 A232557 A119541

Adjacent sequences: A232553 A232554 A232555 * A232557 A232558 A232559

Keyword

nonn

Author

Antonio Roldán, Nov 26 2013

Status

approved