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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
Comment, Feb 12 2012: There are 5255 multiperfect numbers known with multiplicity 3 to 11. No more findings for A091443 so we still have 33 multiperfect numbers divisible by their sofpr (without the trivial case 1). With multiplicity 3..8 quite surely all are found (only very few - if any - missing). It is estimated that there are about 2200 with multiplicity 9 and 2091 of them are already found. With multiplicity 10 of estimated 4500 1161 are known. So far no multiperfect number with multiplicity 9 or 10 is divisible by its sofpr (with repetition). Using sofpr without repetition (A114887), there is one number with multiplicity 9 (or more).
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LINKS
| Sven Simon, Table of n, a(n) for n = 1..33 [Conjectured to be complete]
Achim Flammenkamp, The Multiply Perfect Numbers Page (See here for the latest information about the search)
Eric Weisstein's World of Mathematics, Multiperfect numbers
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EXAMPLE
| a(0): 1379454720 = 2^8*3*5*7*19*37*73, sopfr(n)= 2^5*5
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CROSSREFS
| Cf. A000203, A001414, A005820, A027687, A046060, A046061.
Sequence in context: A172787 A172849 A068746 * A114888 A105015 A185931
Adjacent sequences: A091440 A091441 A091442 * A091444 A091445 A091446
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KEYWORD
| fini,nonn,changed
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AUTHOR
| Sven Simon (sven-h.simon(AT)t-online.de), Jan 10 2004, Feb 12 2012
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