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Search: id:A115350
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| A115350 |
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Termination of the aliquot sequence starting at n. |
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7
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| 1, 2, 3, 3, 5, 6, 7, 7, 3, 7, 11, 3, 13, 7, 3, 3, 17, 11, 19, 7, 11, 7, 23, 17, 6, 3, 13, 28, 29, 3, 31, 31, 3, 7, 13, 17, 37, 7, 17, 43, 41, 3, 43, 43, 3, 3, 47, 41, 7, 43, 11, 3, 53, 3, 17, 41, 23, 31, 59, 43
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Catalan's conjecture [not yet established, and probably false] is that every aliquot sequence terminates in a prime number followed by 1, a perfect number, a friendly pair or an aliquot cycle.
a(n) = the prime number if the sequence terminates in a prime followed by 1, a(n) = a perfect number if the sequence terminates in a perfect number, a(n) = the smallest number of the cycle if the sequence terminates in an aliquot cycle, a(n) = 0 if the sequence is open ended. So far 276 is the smallest number for which the termination of the aliquot sequence is not known.
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LINKS
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W. Creyaufmueller, Aliquot Sequences.
Paul Zimmerman, Aliquot Sequences.
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EXAMPLE
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E.g. a(12)=3 since the aliquot sequence starting at 12 is: 12 - 16 - 15 - 9 - 4 - 3. A(95)=6 since the aliquot sequence starting at 95 is: 95 - 25 - 6 - 6 ...
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CROSSREFS
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Cf. A098007, A098008, A098009, A098010, A003023, A044050, A007906, A037020, A063769, A005114.
Sequence in context: A097247 A097246 A063659 this_sequence A081211 A081213 A081210
Adjacent sequences: A115347 A115348 A115349 this_sequence A115351 A115352 A115353
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KEYWORD
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nonn
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AUTHOR
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Sergio Pimentel (ferdiego(AT)cox.net), Mar 07 2006
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EXTENSIONS
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Edited by njas, Aug 14 2006
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