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Search: id:A067584
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| A067584 |
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Product of divisors of n-th perfect number. |
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+0
1
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| 36, 21952, 30019840638976, 2343612817652433441167245312, 68243196466656578806189194595182660833083134598062479091851170386830226748067289941548778081222656
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is a subsequence of A007955, product of divisors of n.
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FORMULA
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a(n) = A000396(n)^A000043(n) whenever A000396(n) is an even perfect number. (Proof of the existence of odd perfect numbers is a well-known open problem.) A000043(n) is a Mersenne prime.
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EXAMPLE
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a(2) = 21952 because a(2) = 1*2*4*7*14*28=21952 (=28^3) is the product of all (3*2) divisors of the 2nd perfect number, 28 (=2^(3-1) * (2^3 - 1)). a(6), a 169 decimal digit number (=8589869056^17), is the product of all (17*2) divisors of the 6th perfect number, 8589869056 (=2^(17-1) * (2^17 - 1)).
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CROSSREFS
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Cf. A000396, A000043, A007955.
Adjacent sequences: A067581 A067582 A067583 this_sequence A067585 A067586 A067587
Sequence in context: A141475 A134374 A001308 this_sequence A028454 A123397 A023111
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KEYWORD
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easy,nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 31 2002
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