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A335217
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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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2
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6, 56, 60, 70, 72, 80, 88, 90, 104, 736, 800, 832, 928, 992, 1184, 1312, 1376, 1504, 1568, 1696, 1888, 1952, 3230, 3770, 4030, 4510, 5170, 5390, 5800, 5830, 5888, 6808, 7144, 7192, 7400, 7424, 7912, 8056, 8968, 9272, 9656, 9928, 10744, 10792, 11096, 11288, 11392
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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