%I #5 May 25 2020 09:27:13
%S 24,48,54,80,96,112,120,150,160,168,180,192,216,224,240,252,264,270,
%T 280,294,312,320,336,352,360,378,384,396,408,416,432,448,456,468,480,
%U 486,504,528,540,552,560,594,600,612,624,630,640,672,684,696,702,704,720,726
%N Nonunitary Zumkeller numbers: numbers whose set of nonunitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum.
%C Apparently, most of the terms are nonunitary abundant (A064597). Term that are nonunitary deficient (A064598) are 54, 150, 270, 294, 378, ...
%e 24 is a term since its set of nonunitary divisors, {2, 4, 6, 12}, can be partitioned into the two disjoint sets, {2, 4, 6} and {12}, whose sum is equal: 2 + 4 + 6 = 12.
%t nuzQ[n_] := Module[{d = Select[Divisors[n], GCD[#, n/#] > 1 &], sum, x}, sum = Plus @@ d; sum > 0 && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; Select[Range[1000], nuzQ]
%Y Cf. A064591, A064597, A064598, A083207.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 25 2020