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 A061652 Even superperfect numbers: 2^(p-1) where 2^p-1 is a Mersenne prime (A000668). 63
 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, 81129638414606681695789005144064, 85070591730234615865843651857942052864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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, Feb 29 2008 The sum of divisors of a(n) is equal to A000668(n), the n-th Mersenne prime. - Omar E. Pol, Mar 11 2008 Largest proper divisor of A072868(n). - Omar E. Pol, Apr 25 2008 Indices of hexagonal numbers (A000384) that are also even perfect numbers. [Omar E. Pol, 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, Apr 21 2011 If n is in the sequence then n is a solution to the equation phi(sigma(x)) = 2x-2. It seems that there is no other solution to this equation. - Jahangeer Kholdi, Sep 09 2014 The sum of sums of elements of subsets of divisors of a(n), i.e. A229335(a(n)), is a perfect number (A000396). - Jaroslav Krizek, Nov 02 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..18 G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100. Eric Weisstein's World of Mathematics, Superperfect Number Index to divisibility sequences FORMULA a(n) = 2^(A090748(n)). - Lekraj Beedassy, Dec 07 2007 a(n) = (1 + A000668(n))/2. - Omar E. Pol, Mar 11 2008 a(n) = 2^A000043(n)/2 = A072868(n)/2 = A032742(A072868(n)). - Omar E. Pol, Apr 25 2008 MATHEMATICA 2^(Select[Range[512], PrimeQ[2^# - 1] &] - 1) (* Alonso del Arte, Apr 22 2011 *) 2^(MersennePrimeExponent[Range[15]]-1) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 20 2021 *) PROG (PARI) forprime(p=2, 1e3, if(ispseudoprime(2^p-1), print1(2^(p-1)", "))) \\ Charles R Greathouse IV, Mar 14 2012 CROSSREFS Cf. A000043, A000384, A000396, A000668, A019279, A032742, A072868. Sequence in context: A061286 A288756 A019279 * A278913 A306979 A358032 Adjacent sequences: A061649 A061650 A061651 * A061653 A061654 A061655 KEYWORD nonn,nice AUTHOR Jason Earls, Jun 16 2001 STATUS approved

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Last modified September 13 20:16 EDT 2024. Contains 375910 sequences. (Running on oeis4.)