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

2, 3, 5, 7, 29, 349, 359, 3079, 70115921, 514274899, 514277977, 11091501632311

Offset

1,1

Comments

Corresponding quotient primes are 3, 2, 2, 2, 3, 5, 5, 7, 17, 19, 19, 29.

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

Links

Table of n, a(n) for n=1..12.

Example

7 is in the sequence because sigma(7) = 8, pi(7) = 4 and 8/4 = 2 is a prime.

Mathematica

Select[Prime[Range[10^6]], ProvablePrimeQ[DivisorSigma[1, #]/PrimePi[#]] &]
Select[ (* the terms of A052013 *), PrimeQ[(# + 1)/PrimePi@ #] &] (* Robert G. Wilson v, Mar 16 2016 *)

Prog

(PARI) is(n)=my(t=(n+1)/primepi(n)); denominator(t)==1 && isprime(t) && isprime(n) \\ Charles R Greathouse IV, Feb 18 2016
(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

Crossrefs

Subsequence of A052013.

Cf. A000203, A000720.

Sequence in context: A054750 A048404 A052013 * A174536 A054797 A297710

Adjacent sequences: A269019 A269020 A269021 * A269023 A269024 A269025

Keyword

nonn,more

Author

Soumadeep Ghosh, Feb 17 2016

Extensions

a(9)-a(11) from Charles R Greathouse IV, Feb 18 2016

a(12) from Chai Wah Wu, May 25 2018

Status

approved