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A061652
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Even superperfect numbers: 2^(p-1) where 2^p-1 is a Mersenne prime (A000043 and A000668).
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56
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2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, 81129638414606681695789005144064, 85070591730234615865843651857942052864
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is conjectured that there are no odd superperfect numbers, in which case this coincides with A019279.
The number of divisors of a(n) is equal to A000043(n). - Omar E. Pol (info(AT)polprimos.com), Feb 29 2008
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
Largest proper divisor of A075398(n). - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
Indices of hexagonal numbers (A000384) that are also even perfect numbers. [From Omar E. Pol (info(AT)polprimos.com), Aug 26 2008]
Except for the first perfect number 6, this sequence is the greatest common divisor of a perfect number (A000396) and its arithmetic derivative (A003415). - Giorgio Balzarotti greenblue@tiscali.it, Apr 21 2011
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LINKS
| G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
O. E. Pol, Determinacion geometrica de los numeros primos y perfectos".
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n) = 2^(A090748(n)). - Lekraj Beedassy (boodhiman(AT)yahoo.com), Dec 07 2007
a(n)=(1 + A000668(n))/2. - Omar E. Pol (info(AT)polprimos.com), Mar 11 2008
a(n) = 2^A000043(n)/2 = A075398(n)/2 = A032742(A075398(n)). - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
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MATHEMATICA
| 2^(Select[Range[512], PrimeQ[2^# - 1] &] - 1) (* From Alonso del Arte, Apr 22 2011 *)
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CROSSREFS
| Cf. A000043, A000384, A000396, A000668, A019279, A032742, A075398.
Sequence in context: A060656 A061286 A019279 * A162119 A192623 A155519
Adjacent sequences: A061649 A061650 A061651 * A061653 A061654 A061655
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KEYWORD
| nonn,nice
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jun 16 2001
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