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

1,1

Links

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

Example

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.

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]

Crossrefs

The bi-unitary version of A083209.

Subsequence of A335215.

Cf. A335143, A335199, A335202.

Sequence in context: A255853 A183594 A140790 * A335199 A137033 A045526

Adjacent sequences: A335214 A335215 A335216 * A335218 A335219 A335220

Keyword

nonn

Author

Amiram Eldar, May 27 2020

Status

approved