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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Supersequence of A083207.

Sequence in context: A337486 A114989 A362012 * A363171 A336323 A175352

Adjacent sequences: A334163 A334164 A334165 * A334167 A334168 A334169

Keyword

nonn

Author

Ivan N. Ianakiev, Apr 17 2020

Status

approved