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 A335142 Nonunitary Zumkeller numbers: numbers whose set of nonunitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum. 4
 24, 48, 54, 80, 96, 112, 120, 150, 160, 168, 180, 192, 216, 224, 240, 252, 264, 270, 280, 294, 312, 320, 336, 352, 360, 378, 384, 396, 408, 416, 432, 448, 456, 468, 480, 486, 504, 528, 540, 552, 560, 594, 600, 612, 624, 630, 640, 672, 684, 696, 702, 704, 720, 726 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Apparently, most of the terms are nonunitary abundant (A064597). Term that are nonunitary deficient (A064598) are 54, 150, 270, 294, 378, ... LINKS EXAMPLE 24 is a term since its set of nonunitary divisors, {2, 4, 6, 12}, can be partitioned into the two disjoint sets, {2, 4, 6} and {12}, whose sum is equal: 2 + 4 + 6 = 12. MATHEMATICA nuzQ[n_] := Module[{d = Select[Divisors[n], GCD[#, n/#] > 1 &], sum, x}, sum = Plus @@ d; sum > 0 && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; Select[Range[1000], nuzQ] CROSSREFS Cf. A064591, A064597, A064598, A083207. Sequence in context: A040552 A199545 A098427 * A335143 A105651 A105779 Adjacent sequences:  A335138 A335140 A335141 * A335143 A335144 A335145 KEYWORD nonn AUTHOR Amiram Eldar, May 25 2020 STATUS approved

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Last modified August 6 09:38 EDT 2020. Contains 336245 sequences. (Running on oeis4.)