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%I #10 Jun 18 2019 18:24:21
%S 6,12,20,30,42,56,60,66,70,72,78,84,90,102,114,120,138,150,168,174,
%T 180,186,210,220,222,240,246,252,258,272,280,282,294,318,330,354,360,
%U 364,366,390,402,420,426,438,440,462,474,498,510,520,532,534,546,560,570,582,606,618
%N Unitary half-Zumkeller numbers: numbers k whose unitary proper divisors can be partitioned into two disjoint sets whose sums are equal.
%C Unitary divisors of n are divisors d such that gcd(d,n/d)=1.
%C Seemingly, a subsequence of A246198 (half-Zumkeller numbers).
%H Amiram Eldar, <a href="/A290467/b290467.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryDivisorFunction.html">Unitary Divisor Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Unitary_divisor">Unitary divisor</a>
%e The set of unitary proper divisors of 12 is {1,3,4}. It can be partitioned into two disjoint subsets with equal sums of elements: {1,3} and {4}, therefore 12 is in the sequence.
%t uPropDiv[n_/;n>1]:=Block[{d=Most[Divisors[n]]},Select[d,GCD[#,n/#]==1&]];uhZNQ[n_]:=Module[{d=uPropDiv[n],t,ds,x},ds=Plus@@d;If[Mod[ds,2]>0,False,t=CoefficientList[Product[1+x^i,{i,d}],x];t[[1+ds/2]]>0]];Select[Range[10^3],uhZNQ] (* combined from the code by _Robert G. Wilson v_ at A034448 and _T. D. Noe_ at A083207 *)
%Y Cf. A083207, A246198, A290466.
%K nonn
%O 1,1
%A _Ivan N. Ianakiev_, Aug 03 2017
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