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

1,1

Links

Table of n, a(n) for n=1..45.

Example

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.

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]

Crossrefs

Intersection of A290466 and A335142.

Sequence in context: A184075 A207044 A292705 * A063829 A291959 A210643

Adjacent sequences: A335142 A335143 A335144 * A335146 A335147 A335148

Keyword

nonn

Author

Amiram Eldar, May 25 2020

Status

approved