

A335143


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


3



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
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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



