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Bi-unitary Zumkeller numbers (A335215) whose set of bi-unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.
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%I #8 Jun 06 2020 03:17:57

%S 6,56,60,70,72,80,88,90,104,736,800,832,928,992,1184,1312,1376,1504,

%T 1568,1696,1888,1952,3230,3770,4030,4510,5170,5390,5800,5830,5888,

%U 6808,7144,7192,7400,7424,7912,8056,8968,9272,9656,9928,10744,10792,11096,11288,11392

%N Bi-unitary Zumkeller numbers (A335215) whose set of bi-unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.

%H Amiram Eldar, <a href="/A335217/b335217.txt">Table of n, a(n) for n = 1..250</a>

%e 56 is a term since there is only one partition of its set of bi-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 uDivs[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; bDivs[n_] := Select[Divisors[n], Last @ Intersection[uDivs[#], uDivs[n/#]] == 1 &]; bzQ[n_] := Module[{d = bDivs[n], sum, x}, sum = Plus @@ d; If[sum < n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]]; Select[Range[6000], bzQ]

%Y The bi-unitary version of A083209.

%Y Subsequence of A335215.

%Y Cf. A335143, A335199, A335202.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 27 2020