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 A219545 #18 Oct 25 2021 19:51:18
%S A219545 2,2,3,2,3,2,3,2,3,3,2,5,5,3,2,5,5,5,5,5,5,2,5,5,5,5,5,5,5,5,5,5,5,5,
%T A219545 5,5,5,5,5,5,5,5,5,5,5,5,2,5,5,5,5,5,5,5,5,5,5,5,2,5,7,2,5,5,7,5,5,5,
%U A219545 7,7,7,7,5,5,7,7,7,7,5,7,7,7,7,7,7,7,7
%N A219545 Integer values of sigma(n)/n that are prime.
%C A219545 Subsequence of A054030 consisting of primes among the abundancies sigma(m)/m of multiply perfect numbers m (see A007691).
%C A219545 Each 2 corresponds to a perfect number A000396, so if there are infinitely many perfect numbers, then the sequence is infinite.
%C A219545 If, in addition, there are only finitely many multiply perfect numbers m with sigma(m)/m > 2 (see A134639), then a(n) = 2 for all n > some N.
%D A219545 R. K. Guy, Unsolved Problems in Number Theory, B2.
%H A219545 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>
%F A219545 a(n) = sigma(A065997(n))/A065997(n).
%e A219545 A065997(1) = 6 and sigma(6)/6 = (1+2+3+6)/6 = 2, so a(1) = 2.
%t A219545 Select[Table[DivisorSigma[1,n]/n,{n,10^6}],PrimeQ] (* The program only generates the first seven terms of the sequence. To generate them all, the value of n would have to be greatly increased. *) (* _Harvey P. Dale_, Oct 25 2021 *)
%Y A219545 Cf. A000396, A007691, A054030, A065997, A134639.
%K A219545 nonn
%O A219545 1,1
%A A219545 _Jonathan Sondow_, Nov 22 2012
%E A219545 Extended by _T. D. Noe_, Nov 27 2012