Search: id:A019279
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%I A019279
%S A019279 2,4,16,64,4096,65536,262144,1073741824,1152921504606846976
%N A019279 Superperfect numbers: sigma(sigma(n)) = 2n where sigma is the sum-of-divisors 
               function A000203.
%C A019279 Let sigma_m(n) be result of applying sum-of-divisors function m times 
               to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives (2,
               2)-perfect numbers.
%C A019279 Even values of these are 2^(p-1) where 2^p-1 is a Mersenne prime (A000043 
               and A000668). No odd superperfect numbers are known. Hunsucker and 
               Pomerance checked that there are no odd ones below 7 * 10^24.
%C A019279 See also the Cohen-te Reile links under A019276.
%C A019279 The number of divisors of a(n) is equal to A000043(n), if there are no 
               odd superperfect numbers. - Omar E. Pol (info(AT)polprimos.com), 
               Feb 29 2008
%C A019279 The sum of divisors of a(n) is the n-th Mersenne prime A000668(n), provided 
               that there are no odd superperfect numbers. - Omar E. Pol (info(AT)polprimos.com), 
               Mar 11 2008
%C A019279 Largest proper divisor of A075398(n) if there are no odd superperfect 
               numbers. - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
%C A019279 Indices of hexagonal numbers (A000384) that are also even perfect numbers, 
               if there are no odd superperfect numbers. [From Omar E. Pol (info(AT)polprimos.com), 
               Aug 26 2008]
%D A019279 G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, 
               Experimental Mathematics, 5 (1996), pp. 93-100.
%H A019279 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SuperperfectNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A019279 Anonymous, <a href="http://www-maths.swan.ac.uk/pgrads/bb/project/node33.html">
               Superperfect Numbers:Definition</a>
%H A019279 Experimental Mathematics, <a href="http://www.expmath.org/">Home Page</
               a>
%H A019279 O. E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica 
               de los numeros primos y perfectos"</a>.
%F A019279 a(n)=(1 + A000668(n))/2, if there are no odd superperfect numbers. - 
               Omar E. Pol (info(AT)polprimos.com), Mar 11 2008
%F A019279 Also, if there are no odd superperfect numbers then a(n) = 2^A000043(n)/
               2 = A075398(n)/2 = A032742(A075398(n)). - Omar E. Pol (info(AT)polprimos.com), 
               Apr 25 2008
%e A019279 sigma(sigma(4))=2*4, so 4 is in the sequence.
%Y A019279 Cf. A019280, A000203, A000396, A000668, A000043, A034897, A061652.
%Y A019279 Cf. A032742, A075398.
%Y A019279 Cf. A000384. [From Omar E. Pol (info(AT)polprimos.com), Aug 26 2008]
%Y A019279 Sequence in context: A154004 A060656 A061286 this_sequence A061652 A162119 
               A155519
%Y A019279 Adjacent sequences: A019276 A019277 A019278 this_sequence A019280 A019281 
               A019282
%K A019279 nonn,more,nice
%O A019279 1,1
%A A019279 N. J. A. Sloane (njas(AT)research.att.com).
%E A019279 Additional comments and 2 more terms from Jud McCranie (j.mccranie(AT)comcast.net), 
               Jun 01 2000

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