

A335144


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


1



24, 96, 180, 216, 240, 360, 480, 720, 1080, 1440, 2160, 2880, 4320, 5040, 7560, 10080, 15120, 20160, 25200, 30240, 45360, 50400, 60480, 75600, 100800, 110880, 151200, 221760, 277200, 302400, 332640, 453600, 498960, 554400, 665280, 831600, 1108800, 1330560
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OFFSET

1,1


COMMENTS

The corresponding record values are 1, 3, 7, 13, 17, 102, 140, ... (see the link for more values).


LINKS

Table of n, a(n) for n=1..38.
Amiram Eldar, Table of n, a(n), number of ways for n = 1..38


EXAMPLE

24 is the first term since it is the least nonunitary Zumkeller number, and its nonunitary divisors, {2, 4, 6, 12}, can be partitioned in a single way: 2 + 4 + 6 = 12. The next nonunitary Zumkeller number with more than one partition is 96, whose nonunitary divisors, {2, 4, 6, 8, 12, 16, 24, 48}, can be partitioned in 3 ways: 2 + 4 + 6 + 8 + 16 + 24 = 12 + 48, 2 + 6 + 12 + 16 + 24 = 4 + 8 + 48, and 8 + 12 + 16 + 24 = 2 + 4 + 6 + 48.


MATHEMATICA

nuz[n_] := Module[{d = Select[Divisors[n], GCD[#, n/#] > 1 &], sum, x}, sum = Plus @@ d; If[sum < 1  OddQ[sum], 0, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]]/2]]; nuzm = 0; s = {}; Do[nuz1 = nuz[n]; If[nuz1 > nuzm, nuzm = nuz1; AppendTo[s, n]], {n, 1, 8000}]; s


CROSSREFS

The nonunitary version of A083212.
Subsequence of A335142.
Cf. A335143.
Sequence in context: A057102 A057103 A055669 * A209432 A195824 A183009
Adjacent sequences: A335141 A335142 A335143 * A335145 A335146 A335147


KEYWORD

nonn


AUTHOR

Amiram Eldar, May 25 2020


STATUS

approved



