Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Aliquot_sequence> ?p ?o. }
Showing items 1 to 36 of
36
with 100 items per page.
- Aliquot_sequence abstract "In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way: s0 = k sn = σ1(sn−1) − sn−1.For example, the aliquot sequence of 10 is 10, 8, 7, 1, 0 because:σ1(10) − 10 = 5 + 2 + 1 = 8σ1(8) − 8 = 4 + 2 + 1 = 7σ1(7) − 7 = 1σ1(1) − 1 = 0Many aliquot sequences terminate at zero (sequence A080907 in OEIS); all such sequences necessarily end with a prime number followed by 1 (since the only proper divisor of a prime is 1), followed by 0 (since 1 has no proper divisors). There are a variety of ways in which an aliquot sequence might not terminate: A perfect number has a repeating aliquot sequence of period 1. The aliquot sequence of 6, for example, is 6, 6, 6, 6, ... An amicable number has a repeating aliquot sequence of period 2. For instance, the aliquot sequence of 220 is 220, 284, 220, 284, ... A sociable number has a repeating aliquot sequence of period 3 or greater. (Sometimes the term sociable number is used to encompass amicable numbers as well.) For instance, the aliquot sequence of 1264460 is 1264460, 1547860, 1727636, 1305184, 1264460, ... Some numbers have an aliquot sequence which is eventually periodic, but the number itself is not perfect, amicable, or sociable. For instance, the aliquot sequence of 95 is 95, 25, 6, 6, 6, 6, ... . Numbers like 95 that are not perfect, but have an eventually repeating aliquot sequence of period 1 are called aspiring numbers (OEIS A063769).An important conjecture due to Catalan with respect to aliquot sequences is that every aliquot sequence ends in one of the above ways–with a prime number, a perfect number, or a set of amicable or sociable numbers. The alternative would be that a number exists whose aliquot sequence is infinite, yet aperiodic. Any one of the many numbers whose aliquot sequences have not been fully determined might be such a number. The first five candidate numbers are called the Lehmer five (named after Dick Lehmer): 276, 552, 564, 660, and 966.As of December 2013, there were 898 positive integers less than 100,000 whose aliquot sequences have not been fully determined, and 9205 such integers less than 1,000,000.".
- Aliquot_sequence wikiPageExternalLink amicable.homepage.dk.
- Aliquot_sequence wikiPageExternalLink Aliquot.html.
- Aliquot_sequence wikiPageExternalLink aliquote.htm.
- Aliquot_sequence wikiPageExternalLink www.aliquotes.com.
- Aliquot_sequence wikiPageExternalLink 3630finishes1.pdf.
- Aliquot_sequence wikiPageExternalLink forumdisplay.php?f=90.
- Aliquot_sequence wikiPageExternalLink Aliquot000.htm.
- Aliquot_sequence wikiPageID "486266".
- Aliquot_sequence wikiPageRevisionID "584914260".
- Aliquot_sequence hasPhotoCollection Aliquot_sequence.
- Aliquot_sequence subject Category:Arithmetic_functions.
- Aliquot_sequence subject Category:Divisor_function.
- Aliquot_sequence type Abstraction100002137.
- Aliquot_sequence type ArithmeticFunctions.
- Aliquot_sequence type Function113783816.
- Aliquot_sequence type MathematicalRelation113783581.
- Aliquot_sequence type Relation100031921.
- Aliquot_sequence comment "In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term.".
- Aliquot_sequence label "Aliquot sequence".
- Aliquot_sequence label "Inhaltskette".
- Aliquot_sequence label "Sucesión alícuota".
- Aliquot_sequence label "Suite aliquote".
- Aliquot_sequence label "متتالية تجزيئية".
- Aliquot_sequence label "アリコット数列".
- Aliquot_sequence label "真因子和數列".
- Aliquot_sequence sameAs Inhaltskette.
- Aliquot_sequence sameAs Sucesión_alícuota.
- Aliquot_sequence sameAs Suite_aliquote.
- Aliquot_sequence sameAs アリコット数列.
- Aliquot_sequence sameAs m.02g8jf.
- Aliquot_sequence sameAs Q1663510.
- Aliquot_sequence sameAs Q1663510.
- Aliquot_sequence sameAs Aliquot_sequence.
- Aliquot_sequence wasDerivedFrom Aliquot_sequence?oldid=584914260.
- Aliquot_sequence isPrimaryTopicOf Aliquot_sequence.