%I #15 Mar 11 2021 03:32:33
%S 30,42,66,78,102,114,138,150,174,186,210,222,246,258,282,294,318,330,
%T 354,366,390,402,420,426,438,462,474,498,510,534,546,570,582,606,618,
%U 630,642,654,660,678,690,714,726,750,762,770,780,786,798,822,834,840,858
%N Numbers k such that there is a subset of the nontrivial unitary divisors of k, {d|k : 1 < d < k, gcd(d, k/d) = 1}, that adds up to k.
%H Amiram Eldar, <a href="/A342398/b342398.txt">Table of n, a(n) for n = 1..10000</a>
%e 30 is a term since its proper unitary divisors, 1 < d < 30, are {2, 3, 5, 6, 10, 15}, and 5 + 10 + 15 = 30.
%t q[n_] := Module[{d = Most @ Select[Divisors[n], CoprimeQ[#, n/#] &], x}, Plus @@ d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, 2, Length[d]}], {x, 0, n}], n] > 0]; Select[Range[1000], q]
%Y The unitary version of A136446.
%Y Subsequence of A034683 and A293188.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 10 2021