A335201 Unitary Zumkeller numbers (A290466) that are not squarefree.

60, 90, 150, 294, 420, 630, 660, 726, 750, 780, 840, 924, 990, 1014, 1020, 1050, 1092, 1140, 1170, 1380, 1386, 1428, 1470, 1530, 1596, 1638, 1650, 1710, 1734, 1740, 1860, 1890, 1950, 2058, 2070, 2142, 2166, 2220, 2460, 2550, 2580, 2610, 2790, 2820, 2850, 2940

Offset: 1

Author

Amiram Eldar, May 26 2020

Keywords

• nonn

Comments

Zumkeller numbers (A083207) that are squarefree (A005117) are also unitary Zumkeller numbers (A290466), since all of their divisors are unitary.

First differs from A335140 at n = 39.

Examples

			60 is a term since it is nonsquarefree, and its unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, can be partitioned into 2 disjoint sets whose sum is equal: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A290466.

Cf. A005117, A083207.

Programs

Mathematica

uzQ[n_] :=  Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; Select[Range[3000], !SquareFreeQ[#] && uzQ[#] &]