A003604 Number of primes <= n!.

0, 0, 1, 3, 9, 30, 128, 675, 4231, 30969, 258689, 2428956, 25306287, 289620751, 3610490805, 48686912930, 706003798139, 10953617995740, 181035032207760, 3175094503778521, 58893601709552538, 1151825702178908788, 23688535118132456668, 511050155316058710033

Offset: 0

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Keywords

• hard
• nonn

Comments

Number of distinct prime divisors of (n!)!, (A000197). - Jason Earls, Jul 04 2001

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• David Baugh, Table of n, a(n) for n = 0..25 (a(24)-a(25) found using Kim Walisch's primecount program).
• Andrew R. Booker, The Nth Prime Page
• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
• R. G. Wilson v, Letter to N. J. A. Sloane, Oct. 1993
• R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 1993
• R. G. Wilson v, Letter to N. J. A. Sloane, Jan. 1994
• Index entries for sequences related to numbers of primes in various ranges

Crossrefs

Cf. A000040, A000197.

Programs

Mathematica

Table[PrimePi[n!], {n, 0, 16}]

PARI

for(n=0,10,print(omega(n!!)))

PARI

a(n)=primepi(n!) \\ Charles R Greathouse IV, Jan 21 2016

Sage

[prime_pi(factorial(n)) for n in range(0, 14)] # Zerinvary Lajos, Jun 06 2009

Extensions

a(15) from Jud McCranie

a(16)-a(17) from Paul Zimmermann

a(18) from Donovan Johnson, Dec 18 2009

a(19) from Donovan Johnson, Feb 18 2010

a(20) from Henri Lifchitz, Nov 11 2012

a(21)-a(23) from Henri Lifchitz, Aug 26 2014