A335142 Nonunitary Zumkeller numbers: numbers whose set of nonunitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum.

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

Author

Amiram Eldar, May 25 2020

Keywords

• nonn

Comments

Apparently, most of the terms are nonunitary abundant (A064597). Term that are nonunitary deficient (A064598) are 54, 150, 270, 294, 378, ...

Examples

			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.
		

Crossrefs

Cf. A064591, A064597, A064598, A083207.

Programs

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]