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

1,1

Links

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

Example

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.

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]

Crossrefs

The unitary version of A083209.

Subsequence of A290466.

A002827 is a subsequence.

Sequence in context: A308413 A204093 A136927 * A061475 A295830 A335937

Adjacent sequences: A335199 A335200 A335201 * A335203 A335204 A335205

Keyword

nonn

Author

Amiram Eldar, May 26 2020

Extensions

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

Status

approved