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%I #11 May 28 2020 05:27:08
%S 60,90,150,294,420,630,660,726,750,780,840,924,990,1014,1020,1050,
%T 1092,1140,1170,1380,1386,1428,1470,1530,1596,1638,1650,1710,1734,
%U 1740,1860,1890,1950,2058,2070,2142,2166,2220,2460,2550,2580,2610,2790,2820,2850,2940
%N Unitary Zumkeller numbers (A290466) that are not squarefree.
%C Zumkeller numbers (A083207) that are squarefree (A005117) are also unitary Zumkeller numbers (A290466), since all of their divisors are unitary.
%C First differs from A335140 at n = 39.
%H Amiram Eldar, <a href="/A335201/b335201.txt">Table of n, a(n) for n = 1..10000</a>
%e 60 is a term since it is nonsquarefree, and its unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, can be partitioned into 2 disjoint sets whose sum is equal: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
%t uzQ[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; Select[Range[3000], !SquareFreeQ[#] && uzQ[#] &]
%Y Intersection of A013929 and A290466.
%Y Cf. A005117, A083207.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2020
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