%I A061652
%S A061652 2,4,16,64,4096,65536,262144,1073741824,1152921504606846976,309485009821345068724781056,
%T A061652 81129638414606681695789005144064,85070591730234615865843651857942052864
%N A061652 Even superperfect numbers: 2^(p-1) where 2^p-1 is a Mersenne prime (A000043 
               and A000668).
%C A061652 It is conjectured that there are no odd superperfect numbers, in which 
               case this coincides with A019279.
%C A061652 The number of divisors of a(n) is equal to A000043(n). - Omar E. Pol 
               (info(AT)polprimos.com), Feb 29 2008
%C A061652 The sum of divisors of a(n) is equal to A000668(n), the n-th Mersenne 
               prime. - Omar E. Pol (info(AT)polprimos.com), Mar 11 2008
%C A061652 Largest proper divisor of A075398(n). - Omar E. Pol (info(AT)polprimos.com), 
               Apr 25 2008
%C A061652 Indices of hexagonal numbers (A000384) that are also even perfect numbers. 
               [From Omar E. Pol (info(AT)polprimos.com), Aug 26 2008]
%D A061652 G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, 
               Experimental Mathematics, 5 (1996), pp. 93-100.
%H A061652 Experimental Mathematics, <a href="http://www.expmath.org/">Home Page</
               a>
%H A061652 O. E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica 
               de los numeros primos y perfectos"</a>.
%H A061652 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SuperperfectNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A061652 a(n) = 2^(A090748(n)). - Lekraj Beedassy (boodhiman(AT)yahoo.com), Dec 
               07 2007
%F A061652 a(n)=(1 + A000668(n))/2. - Omar E. Pol (info(AT)polprimos.com), Mar 11 
               2008
%F A061652 a(n) = 2^A000043(n)/2 = A075398(n)/2 = A032742(A075398(n)). - Omar E. 
               Pol (info(AT)polprimos.com), Apr 25 2008
%Y A061652 Cf. A000043, A000384, A000396, A000668, A019279, A032742, A075398.
%Y A061652 Sequence in context: A060656 A061286 A019279 this_sequence A162119 A155519 
               A058926
%Y A061652 Adjacent sequences: A061649 A061650 A061651 this_sequence A061653 A061654 
               A061655
%K A061652 nonn,nice
%O A061652 1,1
%A A061652 Jason Earls (zevi_35711(AT)yahoo.com), Jun 16 2001