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A335201
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Unitary Zumkeller numbers (A290466) that are not squarefree.
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1
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60, 90, 150, 294, 420, 630, 660, 726, 750, 780, 840, 924, 990, 1014, 1020, 1050, 1092, 1140, 1170, 1380, 1386, 1428, 1470, 1530, 1596, 1638, 1650, 1710, 1734, 1740, 1860, 1890, 1950, 2058, 2070, 2142, 2166, 2220, 2460, 2550, 2580, 2610, 2790, 2820, 2850, 2940
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OFFSET
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1,1
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COMMENTS
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Zumkeller numbers (A083207) that are squarefree (A005117) are also unitary Zumkeller numbers (A290466), since all of their divisors are unitary.
First differs from A335140 at n = 39.
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LINKS
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EXAMPLE
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60 is a term since it is nonsquarefree, and its unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, can be partitioned 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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uzQ[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, 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[3000], !SquareFreeQ[#] && uzQ[#] &]
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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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