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A342402
Numbers k with property that if k has m proper divisors, there are m/2 proper divisors of k whose sum is k.
0
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.
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
KEYWORD
nonn
AUTHOR
Metin Sariyar, Mar 10 2021
EXTENSIONS
a(8)-a(43) from Alois P. Heinz, Mar 10 2021
STATUS
approved