A335202 Unitary Zumkeller numbers (A290466) whose set of unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.

6, 60, 70, 90, 3230, 3770, 4030, 4510, 5170, 5390, 5830, 50388, 87360, 269990, 442365, 544310, 592670, 740870, 1341230, 1772870, 4173070, 4199030, 5719266, 5728842, 5743206, 34473582, 624032630, 812851182, 1109686930, 1113445430, 2280959890, 55157757606

Offset: 1

Author

Amiram Eldar, May 26 2020

Keywords

• nonn

Examples

			60 is a term since there is only one partition of its set of unitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, into 2 disjoint sets whose sum is equal: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..48 (terms < 10^12)

Crossrefs

The unitary version of A083209.

Subsequence of A290466.

A002827 is a subsequence.

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]] == 2]]; Select[Range[6000], uzQ]

Extensions

Terms a(19) and beyond from Giovanni Resta, May 30 2020