This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A067584 #12 Oct 17 2024 08:23:59 %S A067584 36,21952,30019840638976,2343612817652433441167245312, %T A067584 68243196466656578806189194595182660833083134598062479091851170386830226748067289941548778081222656 %N A067584 Product of divisors of n-th perfect number. %C A067584 This is a subsequence of A007955, product of divisors of n. %H A067584 Amiram Eldar, <a href="/A067584/b067584.txt">Table of n, a(n) for n = 1..8</a> %F A067584 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 exponent. %F A067584 a(n) = A007955(A000396(n)). - _Amiram Eldar_, Oct 17 2024 %e A067584 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)). %e A067584 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)). %t A067584 f[n_] := n^(DivisorSigma[0, n]/2); f /@ PerfectNumber[Range[5]] (* _Amiram Eldar_, Oct 17 2024 *) %Y A067584 Cf. A000396, A000043, A007955. %K A067584 nonn %O A067584 1,1 %A A067584 _Rick L. Shepherd_, Jan 31 2002