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%I #11 May 30 2020 13:51:46
%S 6,60,70,90,3230,3770,4030,4510,5170,5390,5830,50388,87360,269990,
%T 442365,544310,592670,740870,1341230,1772870,4173070,4199030,5719266,
%U 5728842,5743206,34473582,624032630,812851182,1109686930,1113445430,2280959890,55157757606
%N Unitary Zumkeller numbers (A290466) whose set of unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.
%H Giovanni Resta, <a href="/A335202/b335202.txt">Table of n, a(n) for n = 1..48</a> (terms < 10^12)
%e 60 is a term since there is only one partition of its set of unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, 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]] == 2]]; Select[Range[6000], uzQ]
%Y The unitary version of A083209.
%Y Subsequence of A290466.
%Y A002827 is a subsequence.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2020
%E Terms a(19) and beyond from _Giovanni Resta_, May 30 2020
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