A335217 Bi-unitary Zumkeller numbers (A335215) whose set of bi-unitary divisors can be partitioned into two disjoint sets of equal sum in a single way.

6, 56, 60, 70, 72, 80, 88, 90, 104, 736, 800, 832, 928, 992, 1184, 1312, 1376, 1504, 1568, 1696, 1888, 1952, 3230, 3770, 4030, 4510, 5170, 5390, 5800, 5830, 5888, 6808, 7144, 7192, 7400, 7424, 7912, 8056, 8968, 9272, 9656, 9928, 10744, 10792, 11096, 11288, 11392

Offset: 1

Author

Amiram Eldar, May 27 2020

Keywords

• nonn

Examples

			56 is a term since there is only one partition of its set of bi-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

• Amiram Eldar, Table of n, a(n) for n = 1..250

Crossrefs

The bi-unitary version of A083209.

Subsequence of A335215.

Cf. A335143, A335199, A335202.

Programs

Mathematica

uDivs[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; bDivs[n_] := Select[Divisors[n], Last @ Intersection[uDivs[#], uDivs[n/#]] == 1 &]; bzQ[n_] := Module[{d = bDivs[n], sum, x}, sum = Plus @@ d; If[sum < n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]]; Select[Range[6000], bzQ]