A067584 Product of divisors of n-th perfect number.

36, 21952, 30019840638976, 2343612817652433441167245312, 68243196466656578806189194595182660833083134598062479091851170386830226748067289941548778081222656

Offset

1,1

Comments

This is a subsequence of A007955, product of divisors of n.

Links

Table of n, a(n) for n=1..5.

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