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%I #9 Jun 30 2020 05:33:34
%S 6,24,30,40,42,54,56,60,66,70,72,78,88,90,96,102,104,114,120,138,150,
%T 168,174,186,210,216,222,246,258,264,270,280,282,294,312,318,330,354,
%U 360,366,378,384,390,402,408,420,426,438,440,456,462,474,480,486,498,504
%N Infinitary Zumkeller numbers: numbers whose set of infinitary divisors can be partitioned into two disjoint sets of equal sum.
%H Amiram Eldar, <a href="/A335197/b335197.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 is a term since its set of infinitary divisors, {1, 2, 3, 6}, can be partitioned into the two disjoint sets, {1, 2, 3} and {6}, whose sum is equal: 1 + 2 + 3 = 6.
%t infdivs[n_] := If[n == 1, {1}, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infZumQ[n_] := Module[{d = infdivs[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[500], infZumQ] (* after _Michael De Vlieger_ at A077609 *)
%Y The infinitary version of A083207.
%Y Subsequence of A129656.
%Y Cf. A077609, A323344.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2020
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