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- Sociable_number abstract "Sociable numbers are numbers whose aliquot sums form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of amicable numbers and perfect numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. In a set of sociable numbers, each number is the sum of the proper factors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point.The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle.If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of order 2. There are no known sociable numbers of order 3.It is an open question whether all numbers end up at either a sociable number or at a prime (and hence 1), or, equivalently, whether there exist numbers whose aliquot sequence never terminates, and hence grows without bound.".
- Sociable_number wikiPageExternalLink tables.htm.
- Sociable_number wikiPageExternalLink sociable.txt.
- Sociable_number wikiPageID "332307".
- Sociable_number wikiPageLength "4396".
- Sociable_number wikiPageOutDegree "27".
- Sociable_number wikiPageRevisionID "703790756".
- Sociable_number wikiPageWikiLink Aliquot_sequence.
- Sociable_number wikiPageWikiLink Aliquot_sum.
- Sociable_number wikiPageWikiLink Amicable_numbers.
- Sociable_number wikiPageWikiLink Belgium.
- Sociable_number wikiPageWikiLink Category:Divisor_function.
- Sociable_number wikiPageWikiLink Category:Integer_sequences.
- Sociable_number wikiPageWikiLink Category:Number_theory.
- Sociable_number wikiPageWikiLink Cycle_(graph_theory).
- Sociable_number wikiPageWikiLink Directed_graph.
- Sociable_number wikiPageWikiLink Divisor.
- Sociable_number wikiPageWikiLink Frequency.
- Sociable_number wikiPageWikiLink LIntermxc3xa9diaire_des_Mathxc3xa9maticiens.
- Sociable_number wikiPageWikiLink Mathematics.
- Sociable_number wikiPageWikiLink Oeis:A003416.
- Sociable_number wikiPageWikiLink Oeis:A122726.
- Sociable_number wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Sociable_number wikiPageWikiLink Paul_Poulet.
- Sociable_number wikiPageWikiLink Perfect_number.
- Sociable_number wikiPageWikiLink Prime_number.
- Sociable_number wikiPageWikiLinkText "Sociable number".
- Sociable_number wikiPageWikiLinkText "sociable chain".
- Sociable_number wikiPageWikiLinkText "sociable number".
- Sociable_number wikiPageWikiLinkText "sociable".
- Sociable_number title "Sociable numbers".
- Sociable_number urlname "SociableNumbers".
- Sociable_number wikiPageUsesTemplate Template:Classes_of_natural_numbers.
- Sociable_number wikiPageUsesTemplate Template:Divisor_classes.
- Sociable_number wikiPageUsesTemplate Template:Mathworld.
- Sociable_number wikiPageUsesTemplate Template:Reflist.
- Sociable_number subject Category:Divisor_function.
- Sociable_number subject Category:Integer_sequences.
- Sociable_number subject Category:Number_theory.
- Sociable_number hypernym Numbers.
- Sociable_number type Plant.
- Sociable_number type Combinatoric.
- Sociable_number type Field.
- Sociable_number type Function.
- Sociable_number type Integer.
- Sociable_number comment "Sociable numbers are numbers whose aliquot sums form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of amicable numbers and perfect numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. In a set of sociable numbers, each number is the sum of the proper factors of the preceding number, i.e., the sum excludes the preceding number itself.".
- Sociable_number label "Sociable number".
- Sociable_number sameAs Q1149466.
- Sociable_number sameAs Nombres_sociables.
- Sociable_number sameAs Societema_nombro.
- Sociable_number sameAs Números_sociables.
- Sociable_number sameAs Nombre_sociable.
- Sociable_number sameAs Números_sociables.
- Sociable_number sameAs מספרים_חברותיים.
- Sociable_number sameAs Társas_számok.
- Sociable_number sameAs Numero_socievole.
- Sociable_number sameAs 社交数.
- Sociable_number sameAs 사교수.
- Sociable_number sameAs Numerus_sociabilis.
- Sociable_number sameAs Nùmer_socévol.
- Sociable_number sameAs m.01x1hw.
- Sociable_number sameAs Družabno_število.
- Sociable_number sameAs Q1149466.
- Sociable_number sameAs 相亲数链.
- Sociable_number wasDerivedFrom Sociable_number?oldid=703790756.
- Sociable_number isPrimaryTopicOf Sociable_number.