A335143 Nonunitary Zumkeller numbers (A335142) whose set of nonunitary divisors can be partitioned into two disjoint sets of equal sum in a single way.

24, 48, 54, 80, 112, 150, 224, 280, 294, 352, 416, 630, 704, 726, 832, 1014, 1088, 1216, 1472, 1734, 1750, 1856, 1984, 2166, 2475, 2944, 3174, 3344, 3430, 3712, 3968, 4275, 4736, 5046, 5248, 5504, 5766, 6016, 6784, 7552, 7808, 8214, 8470, 10086, 11008, 11094

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

24 is a term since there is only one partition of its set of nonunitary divisors, {2, 4, 6, 12}, into two disjoint sets of equal sum: {2, 4, 6} and {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]] == 2]; Select[Range[12000], nuzQ]

Crossrefs

The nonunitary version of A083209.

Subsequence of A335142.

Sequence in context: A199545 A098427 A335142 * A105651 A105779 A199105

Adjacent sequences: A335140 A335141 A335142 * A335144 A335145 A335146

Keyword

nonn

Author

Amiram Eldar, May 25 2020

Status

approved