%I #4 May 27 2020 01:59:00
%S 6,56,60,70,72,88,90,104,3040,3230,3770,4030,4510,5170,5390,5800,5830,
%T 6808,7144,7192,7400,7912,8056,8968,9272,9656,9928,10744,10792,11016,
%U 11096,11288,11392,12104,12416,12928,13184,13192,13696,13736,13952,14008,14464,14552
%N Infinitary Zumkeller numbers (A335197) whose set of infinitary divisors can be partitioned into two disjoint sets of equal sum in a single way.
%e 6 is a term since there is only one partition of its set of nonunitary divisors, {1, 2, 3, 6}, into two disjoint sets of equal sum: {1, 2, 3} and {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]] == 2]]; Select[Range[15000], infZumQ] (* after _Michael De Vlieger_ at A077609 *)
%Y The infinitary version of A083209.
%Y Subsequence of A335197.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2020