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

1,1

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.

Links

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

Example

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.

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[#] &]

Crossrefs

Intersection of A013929 and A290466.

Cf. A005117, A083207.

Sequence in context: A110546 A378054 A335140 * A267434 A048934 A097714

Adjacent sequences: A335198 A335199 A335200 * A335202 A335203 A335204

Keyword

nonn

Author

Amiram Eldar, May 26 2020

Status

approved