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Search: id:A091443
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| A091443 |
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Multiperfect numbers n which are divisible by sopfr(n) (multiperfect number: sigma(n) = k*n with k integer, sopfr: Sum of prime factors with repetition). Ordered by size of n. |
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3
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| 1379454720, 14182439040, 212517062615531520, 27099073228001299660800, 680489641226538823680000, 15229814702070563916152832000, 34111227434420791224041472000, 59023729003862626557345792000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence contains multiperfect numbers with multiplicity k from 3..8. They are extracted from a list with about 5000 multiperfect numbers with multiplicity from 2..11. Because of the size of these numbers, no numbers with multiplicity k > 8 were found, even though there were about 3000 of them in the list. 95% of the multiperfect numbers with multiplicity from 3..8 are known. Conjecture: the sequence is finite.
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LINKS
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Sven Simon, Table of n, a(n) for n = 1..33 [Conjectured to be complete]
Achim Flammenkamp, List with multiperfect numbers
Eric Weisstein's World of Mathematics, Multiperfect numbers
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EXAMPLE
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a(0): 1379454720 = 2^8*3*5*7*19*37*73, sopfr(n)= 2^5*5
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CROSSREFS
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Cf. A000203, A001414, A005820, A027687, A046060, A046061.
Sequence in context: A100004 A113641 A068746 this_sequence A114888 A105015 A069320
Adjacent sequences: A091440 A091441 A091442 this_sequence A091444 A091445 A091446
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KEYWORD
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fini,nonn
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AUTHOR
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Sven Simon (sven-h.simon(AT)t-online.de), Jan 10 2004
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