Search: id:A061644
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%I A061644
%S A061644 7,29,33550337,137438691329
%N A061644 "Right perfect numbers": primes of the form 1 + a perfect number.
%C A061644 Readers of Rivera's web page (which I believe was indirectly based on 
               this entry) later showed that there are no more cases among the first 
               39 perfect numbers. - N. J. A. Sloane (njas(AT)research.att.com), 
               May 25 2004. The latest news is that there are no more cases among 
               the first 44 perfect numbers - Maximilian Hasler, Jun 05 2008.
%C A061644 So of the 44 known perfect numbers P=2^(p-1)*(2^p-1), P+1 is only prime 
               for p=2,3,13 and 19.
%H A061644 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_203.htm">
               Puzzle 203</a>
%H A061644 Mersenne Forum, <a href="http://www.mersenneforum.org/showthread.php?t=10336">
               Thread 10336</a>
%F A061644 P(p)*[P(p)+1]/2 is prime, where P(p) is a Mersenne prime.
%F A061644 P(p)*[P(p)+1]/2 + 1 is prime, where P(p) is a Mersenne prime.(Rectified) 
               [From Lekraj Beedassy (blekraj(AT)yahoo.com), May 01 2009]
%t A061644 pn={6,28,496,8128,33550336,8589869056,137438691328,2305843008139952128,
               2658455991569831744654692615953842176,191561942608236107294793378084303638130997321548169216};
               lst={};Do[p=pn[[n]]+1;If[PrimeQ[p],AppendTo[lst,p]],{n,Length[pn]}];
               lst... and/or...PerfectNum[n_]:=Plus@@Divisors[n]/2;lst={};Do[p=PerfectNum[n];
               If[p==n&&PrimeQ[p+1],AppendTo[lst,p+1]],{n,10!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jan 27 2009]
%Y A061644 Cf. A000396.
%Y A061644 Analogous right and left multiple perfect numbers are in A093034, A094467.
%Y A061644 Sequence in context: A135629 A122119 A157422 this_sequence A053621 A018831 
               A063128
%Y A061644 Adjacent sequences: A061641 A061642 A061643 this_sequence A061645 A061646 
               A061647
%K A061644 more,nonn
%O A061644 1,1
%A A061644 Labos E. (labos(AT)ana.sote.hu), Jun 14 2001

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