A334166 Numbers k having a divisor d, such that d*k is a Zumkeller number (A083207).

6, 10, 12, 14, 18, 20, 24, 28, 30, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 66, 68, 70, 72, 76, 78, 80, 84, 88, 90, 92, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 116, 120, 124, 126, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176, 180, 182, 184, 186, 190

Offset: 1

Author

Ivan N. Ianakiev, Apr 17 2020

Keywords

• nonn

Comments

Conjecture: The difference between two consecutive terms is 6 at most.

Examples

			2 is a divisor of 10 and 10 is not a Zumkeller number, but 2*10 = 20 is a Zumkeller number, therefore 10 is in the sequence.
		

Links

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

Crossrefs

Supersequence of A083207.

Programs

Mathematica

zQ[n_]:=Module[{d=Divisors[n],t,ds,x},ds=Plus@@d;If[Mod[ds,2]>0,False,t=CoefficientList[Product[1+x^i,{i,d}],x];t[[1+ds/2]]>0]]; fQ[n_]:=AnyTrue[n*Divisors[n],zQ];
Select[Range[200],fQ] (* zQ defined by T. D. Noe at A083207 *)