A335145 Numbers that are both unitary and nonunitary Zumkeller numbers.
150, 294, 630, 726, 750, 840, 1014, 1050, 1470, 1650, 1734, 1890, 1950, 2058, 2166, 2550, 2850, 2940, 2970, 3174, 3234, 3450, 3510, 3630, 3750, 3822, 4350, 4410, 4650, 4998, 5046, 5070, 5082, 5250, 5550, 5586, 5670, 5766, 6150, 6450, 6762, 6930, 7050, 7098, 7260
Offset: 1
Keywords
Examples
150 is a term since its unitary divisors, {1, 2, 3, 6, 25, 50, 75, 150} can be partitioned in two disjoint sets of equal sum: 1 + 2 + 3 + 25 + 50 + 75 = 6 + 150, and so are its nonunitary divisors, {5, 10, 15, 30}: 5 + 10 + 15 = 30.
Programs
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Mathematica
zumQ[n_] := Module[{d = Divisors[n], ud, nd, sumUd, sumNd, x},ud = Select[d, CoprimeQ[#, n/#] &]; nd = Complement[d, ud]; sumUd = Plus @@ ud; sumNd = Plus @@ nd; sumUd >= 2*n && sumNd > 0 && EvenQ[sumUd] && EvenQ[sumNd] && CoefficientList[Product[1 + x^i, {i, ud}], x][[1 + sumUd/2]] > 0 && CoefficientList[Product[1 + x^i, {i, nd}], x][[1 + sumNd/2]] > 0]; Select[Range[10000], zumQ]