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A067584
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Product of divisors of n-th perfect number.
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1
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OFFSET
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1,1
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COMMENTS
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This is a subsequence of A007955, product of divisors of n.
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LINKS
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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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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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