OFFSET
1,1
COMMENTS
First differs from A343311 at n = 29.
Differs from A080257 which contains for example 8 and 128. - R. J. Mathar, Nov 03 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
6 is a term since its set of divisors, {1, 2, 3, 6}, can be partitioned into the two disjoint sets {1, 3} and {2, 6} whose arithmetic means, 2 and 4 respectively, are both integers.
MATHEMATICA
amQ[d_] := IntegerQ @ Mean[d]; q[n_] := Module[{d = Divisors[n], nd, s, subs, ans = False}, nd = Length[d]; subs = Subsets[d]; Do[s = subs[[k]]; If[Length[s] > 1 && Length[s] <= nd/2 && amQ[s] && amQ[Complement[d, s]], ans = True; Break[]], {k, 1, Length[subs]}]; ans]; Select[Range[100], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 31 2021
STATUS
approved