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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.
6
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
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, ...
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 25 2020
STATUS
approved