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
Keywords
Examples
576 is a term because it has 20 proper divisors and 1+2+3+4+6+8+24+48+192+288 = 576.
Programs
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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 *)
Extensions
a(8)-a(43) from Alois P. Heinz, Mar 10 2021
Comments