A342402 Numbers k with property that if k has m proper divisors, there are m/2 proper divisors of k whose sum is k.

36, 100, 144, 324, 400, 576, 784, 900, 1296, 1600, 1764, 1936, 2304, 2500, 2704, 2916, 3136, 3600, 4356, 4624, 4900, 5184, 5776, 6084, 6400, 7056, 7744, 8100, 9216, 9604, 10000, 10404, 10816, 11025, 11664, 12100, 12544, 12996, 14400, 15876, 16900, 17424, 18496

Offset

1,1

Comments

All terms are perfect squares.

Links

Table of n, a(n) for n=1..43.

Example

576 is a term because it has 20 proper divisors and 1+2+3+4+6+8+24+48+192+288 = 576.

Mathematica

q[n_] := Module[{d = Most @ Divisors[n], nd, ans = False}, nd = Length[d]; Do[If[Plus @@ Subsets[d, {nd/2}, {k}][[1]] == n, ans = True; Break[]], {k, 1, Binomial[nd, nd/2]}]; ans]; Select[Range[136]^2, q] (* Amiram Eldar, Mar 11 2021 *)

Crossrefs

Cf. A000396, A001065, A005835, A293188, A342119.

Sequence in context: A296204 A063734 A069057 * A348826 A062703 A043438

Adjacent sequences: A342399 A342400 A342401 * A342403 A342404 A342405

Keyword

nonn

Author

Metin Sariyar, Mar 10 2021

Extensions

a(8)-a(43) from Alois P. Heinz, Mar 10 2021

Status

approved