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

Author

Soumadeep Ghosh, Feb 17 2016

Keywords

• nonn
• more

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

Examples

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

Crossrefs

Subsequence of A052013.

Cf. A000203, A000720.

Programs

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 *)

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

Extensions

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

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