A335215 Bi-unitary Zumkeller numbers: numbers whose set of bi-unitary divisors can be partitioned into two disjoint sets of equal sum.

6, 24, 30, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 88, 90, 96, 102, 104, 114, 120, 138, 150, 160, 162, 168, 174, 186, 192, 210, 216, 222, 224, 240, 246, 258, 264, 270, 280, 282, 288, 294, 312, 318, 320, 330, 336, 352, 354, 360, 366, 378, 384, 390, 402

Offset

1,1

Links

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

Example

6 is a term since its set of bi-unitary divisors, {1, 2, 3, 6}, can be partitioned into 2 disjoint sets, whose sum is equal: 1 + 2 + 3 = 6.

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 < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; Select[Range[10^3], bzQ]

Crossrefs

The bi-unitary version of A083207.

Subsequence of A292982.

Cf. A188999, A222266, A290466, A323342, A335142, A335197.

Sequence in context: A228383 A249667 A114274 * A292985 A335197 A364053

Adjacent sequences: A335212 A335213 A335214 * A335216 A335217 A335218

Keyword

nonn

Author

Amiram Eldar, May 27 2020

Status

approved