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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding record values are 1, 3, 7, 13, 17, 102, 140, ... (see the link for more values). LINKS 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

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Last modified October 1 12:58 EDT 2020. Contains 337443 sequences. (Running on oeis4.)