A003604 Number of primes <= n!. (Formerly M2815)

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

0,4

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A000197.

Sequence in context: A297198 A297202 A370439 * A357615 A292300 A058148

Adjacent sequences: A003601 A003602 A003603 * A003605 A003606 A003607

Keyword

hard,nonn

Author

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

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

Status

approved