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 A067584 Product of divisors of n-th perfect number. 1
 36, 21952, 30019840638976, 2343612817652433441167245312, 68243196466656578806189194595182660833083134598062479091851170386830226748067289941548778081222656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a subsequence of A007955, product of divisors of n. LINKS FORMULA 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. EXAMPLE 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)). CROSSREFS Cf. A000396, A000043, A007955. Sequence in context: A203329 A271338 A001308 * A308423 A146521 A159431 Adjacent sequences:  A067581 A067582 A067583 * A067585 A067586 A067587 KEYWORD easy,nonn AUTHOR Rick L. Shepherd, Jan 31 2002 STATUS approved

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Last modified January 29 05:09 EST 2022. Contains 350672 sequences. (Running on oeis4.)