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

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

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: A335139 A335140 A335141 * A335143 A335144 A335145

Keyword

nonn

Author

Amiram Eldar, May 25 2020

Status

approved