A335215 - OEIS

%I #12 May 31 2020 02:12:42

%S 6,24,30,40,42,48,54,56,60,66,70,72,78,80,88,90,96,102,104,114,120,

%T 138,150,160,162,168,174,186,192,210,216,222,224,240,246,258,264,270,

%U 280,282,288,294,312,318,320,330,336,352,354,360,366,378,384,390,402

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

%H Amiram Eldar, <a href="/A335215/b335215.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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]

%Y The bi-unitary version of A083207.

%Y Subsequence of A292982.

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

%K nonn

%O 1,1

%A _Amiram Eldar_, May 27 2020