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

1,1

Links

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

Example

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

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[100000], !IntegerQ[Sqrt[#]] && sqQ[A035316[#]] &] (* Amiram Eldar, Aug 12 2023 *)

Prog

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

Crossrefs

Subsequence of A232556.

Cf. A232554, A232557.

Sequence in context: A241240 A035897 A064256 * A330841 A035779 A108003

Adjacent sequences: A232552 A232553 A232554 * A232556 A232557 A232558

Keyword

nonn

Author

Antonio Roldán, Nov 26 2013

Status

approved