Nondividing Set

Author

Eric W. Weisstein
June 29, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/NondividingSet.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/NondividingSet.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<DiscreteMath`Combinatorica`;
<<EISFormat`;

Definitions

NondividingQuotients[l_List]:=Union[Plus@@@Select[Subsets[l],Length[#]>1&]]

NondividingQ[l_List]:=!IntegerQ/@Or@@Flatten[Outer[Divide,NondividingQuotients[l],l]]

Nondividing

NondividingQ[{}]

NondividingQ/@List/@Range[10]

{#,MemberQ[#,1],NondividingQ[#],MemberQ[#,1]&&!NondividingQ[#]}&/@Subsets[Range[4]]//ColumnForm

NondividingQ[{2,3,5}]

NondividingQ[{4,6,7}]

Sort[Select[Subsets[6],NondividingQ[#]&]]

FormatSequence[
Table[Count[NondividingQ/@Subsets[Range[n]],True],
{n,0,11}],51014,0,
Name->"Number of nondividing sets on {1,2,...,n}.",
html["NondividingSet"]
]