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%I #33 May 30 2018 08:03:16
%S 2,3,5,7,29,349,359,3079,70115921,514274899,514277977,11091501632311
%N Primes p such that sigma(p)/pi(p) is prime.
%C Corresponding quotient primes are 3, 2, 2, 2, 3, 5, 5, 7, 17, 19, 19, 29.
%C a(13) > 8.1*10^13 if it exists. Assuming the Riemann Hypothesis, a(13) > 3.27*10^16 (if it exists). - _Chai Wah Wu_, May 25 2018
%e 7 is in the sequence because sigma(7) = 8, pi(7) = 4 and 8/4 = 2 is a prime.
%t Select[Prime[Range[10^6]], ProvablePrimeQ[DivisorSigma[1, #]/PrimePi[#]] &]
%t Select[ (* the terms of A052013 *), PrimeQ[(# + 1)/PrimePi@ #] &] (* _Robert G. Wilson v_, Mar 16 2016 *)
%o (PARI) is(n)=my(t=(n+1)/primepi(n)); denominator(t)==1 && isprime(t) && isprime(n) \\ _Charles R Greathouse IV_, Feb 18 2016
%o (PARI) list(lim)=my(v=List(),n,t); forprime(p=2,lim, t=(p+1)/n++; if(denominator(t)==1 && isprime(t), listput(v, p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 18 2016
%Y Subsequence of A052013.
%Y Cf. A000203, A000720.
%K nonn,more
%O 1,1
%A _Soumadeep Ghosh_, Feb 17 2016
%E a(9)-a(11) from _Charles R Greathouse IV_, Feb 18 2016
%E a(12) from _Chai Wah Wu_, May 25 2018
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