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%I #4 Mar 30 2012 17:36:38
%S 36,21952,30019840638976,2343612817652433441167245312,
%T 68243196466656578806189194595182660833083134598062479091851170386830226748067289941548778081222656
%N Product of divisors of n-th perfect number.
%C This is a subsequence of A007955, product of divisors of n.
%F 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.
%e 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)).
%Y Cf. A000396, A000043, A007955.
%K easy,nonn
%O 1,1
%A _Rick L. Shepherd_, Jan 31 2002
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