This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A189373 #34 Jul 09 2025 10:16:10
%S A189373 6,28,33550336,137438691328
%N A189373 Perfect numbers k such that k+1 is prime.
%C A189373 _Joerg Arndt_ checked that up to exponent p=110503 of the corresponding Mersenne prime 2^p - 1 the number k=2^(p-1)*(2^p-1)+1 is not pseudoprime.
%C A189373 The listed perfect numbers have exponents p in 2, 3, 13, 19.
%H A189373 MathOverflow, <a href="http://mathoverflow.net/questions/62797/even-perfect-numbers-n-with-n1-prime">Even perfect numbers n with n+1 prime</a>.
%F A189373 a(n) = A061644(n) - 1. - _Amiram Eldar_, May 06 2024
%e A189373 We have a(3) = 33550336 since 33550337 is prime and there is no other such perfect number less than a(3) and that exceeds a(2) = 28.
%o A189373 (PARI)
%o A189373 {e=[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787];} /* exponents of Mersenne primes */
%o A189373 for(n=1,#e,p=(2^e[n]-1)*(2^(e[n]-1));if(ispseudoprime(p+1),print1(p,", ")));
%Y A189373 Cf. A000396, A061644, A099057.
%K A189373 nonn,bref,hard
%O A189373 1,1
%A A189373 _Luis H. Gallardo_, Apr 23 2011