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%I #18 Oct 25 2021 19:51:18
%S 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 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 7,7,7,7,5,5,7,7,7,7,5,7,7,7,7,7,7,7,7
%N Integer values of sigma(n)/n that are prime.
%C Subsequence of A054030 consisting of primes among the abundancies sigma(m)/m of multiply perfect numbers m (see A007691).
%C Each 2 corresponds to a perfect number A000396, so if there are infinitely many perfect numbers, then the sequence is infinite.
%C 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 R. K. Guy, Unsolved Problems in Number Theory, B2.
%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>
%F a(n) = sigma(A065997(n))/A065997(n).
%e A065997(1) = 6 and sigma(6)/6 = (1+2+3+6)/6 = 2, so a(1) = 2.
%t 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 Cf. A000396, A007691, A054030, A065997, A134639.
%K nonn
%O 1,1
%A _Jonathan Sondow_, Nov 22 2012
%E Extended by _T. D. Noe_, Nov 27 2012
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