1,1

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. - njas, May 25 2004. The latest news is that there are no more cases among the first 44 perfect numbers - Maximilian Hasler, Jun 05 2008.

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.

C. Rivera, Puzzle 203

Mersenne Forum, Thread 10336

P(p)*[P(p)+1]/2 is prime, where P(p) is a Mersenne prime.

Cf. A000396.

Analogous right and left multiple perfect numbers are in A093034, A094467.

Sequence in context: A120789 A135629 A122119 this_sequence A053621 A018831 A063128

Adjacent sequences: A061641 A061642 A061643 this_sequence A061645 A061646 A061647

more,nonn

Labos E. (labos(AT)ana.sote.hu), Jun 14 2001