Sociable Numbers

Author

Eric W. Weisstein
March 1, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/SociableNumbers.nb.

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Order 4

str=Table[Import["http://amicable.adsl.dk/aliquot/c4/c4_"<>ToString[n]<>".txt","Text"],{n,53}];

order4=Flatten[Map[First[StringSplit[#,"="]]&/@(StringSplit[#,"\n"][[2]]&/@StringSplit[#,"\n\n"])&,DeleteCases[str,$Failed],{1}]]

Length[order4]

Enumeration

sociable=Select[SociableIndices,IntegerQ]

(s={#,Length[Sociable[#]]}&/@sociable)//TableForm

Total[s[[All,-1]]]

See http://amicable.homepage.dk/knwnc4.htm

Tally[IntegerLength/@Sociable[4]]

TableForm[{#,If[Length[s=Sociable[#]]>10,Take[s,10],s]}&/@sociable,
TableDepth->2]

Checks

(orders=Map[SociableOrder,Sociable/@sociable,{2}])//Column//Timing

Map[Min[AliquotSequence[#]]&,Sociable/@sociable,{2}]==Sociable/@sociable//Timing

1/m-Sociable (Kohmoto)

AliquotSequence[#,2,3]&/@mSociable[3,2]

AliquotSequence[#,2,4]&/@mSociable[4,2]

AliquotSequence[#,12,4]&/@mSociable[4,12]