A166678 a(n) = pi((sqrt(P(n))+1)^2) - pi(P(n)), where pi(n) = number of primes <= n and P(n) = n-th primorial.

2, 2, 3, 6, 14, 34, 110, 384, 1540, 7019, 34501, 183439, 1045196, 6164423, 38285946

Offset: 1

Author

Daniel Tisdale, Oct 18 2009, Oct 23 2009

Keywords

• nonn
• more
• less

Comments

Conjecture: pi((sqrt(P(n))+1)^2) - pi(P(n)) >= n.

Crossrefs

Cf. A000720 (pi), A002110 (primorials), A000849 (pi(primorials)).

Programs

Mathematica

a[n_] := Product[Prime[k], {k, 1, n}]; Table[PrimePi[(Sqrt[a[n]] + 1)^2] - PrimePi[a[n]], {n, 1, 12}] (* G. C. Greubel, May 22 2016 *)

PARI

a(n) = my(P=vecprod(primes(n))); primepi((sqrt(P)+1)^2) - primepi(P); \\ Michel Marcus, Aug 15 2022

Extensions

a(13)-a(15) from Ray Chandler, May 10 2010

Name edited by Michel Marcus, Aug 15 2022