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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.

A269022 Primes p such that sigma(p)/pi(p) is prime.

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%I A269022 #33 May 30 2018 08:03:16
%S A269022 2,3,5,7,29,349,359,3079,70115921,514274899,514277977,11091501632311
%N A269022 Primes p such that sigma(p)/pi(p) is prime.
%C A269022 Corresponding quotient primes are 3, 2, 2, 2, 3, 5, 5, 7, 17, 19, 19, 29.
%C A269022 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 A269022 7 is in the sequence because sigma(7) = 8, pi(7) = 4 and 8/4 = 2 is a prime.
%t A269022 Select[Prime[Range[10^6]], ProvablePrimeQ[DivisorSigma[1, #]/PrimePi[#]] &]
%t A269022 Select[ (* the terms of A052013 *), PrimeQ[(# + 1)/PrimePi@ #] &] (* _Robert G. Wilson v_, Mar 16 2016 *)
%o A269022 (PARI) is(n)=my(t=(n+1)/primepi(n)); denominator(t)==1 && isprime(t) && isprime(n) \\ _Charles R Greathouse IV_, Feb 18 2016
%o A269022 (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 A269022 Subsequence of A052013.
%Y A269022 Cf. A000203, A000720.
%K A269022 nonn,more
%O A269022 1,1
%A A269022 _Soumadeep Ghosh_, Feb 17 2016
%E A269022 a(9)-a(11) from _Charles R Greathouse IV_, Feb 18 2016
%E A269022 a(12) from _Chai Wah Wu_, May 25 2018