cp's OEIS Frontend

A003604 Number of primes <= n!.

%I A003604 M2815 #85 Apr 03 2023 10:36:09
%S A003604 0,0,1,3,9,30,128,675,4231,30969,258689,2428956,25306287,289620751,
%T A003604 3610490805,48686912930,706003798139,10953617995740,181035032207760,
%U A003604 3175094503778521,58893601709552538,1151825702178908788,23688535118132456668,511050155316058710033
%N A003604 Number of primes <= n!.
%C A003604 Number of distinct prime divisors of (n!)!, (A000197). - _Jason Earls_, Jul 04 2001
%D A003604 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003604 David Baugh, <a href="/A003604/b003604.txt">Table of n, a(n) for n = 0..25</a> (a(24)-a(25) found using Kim Walisch's primecount program).
%H A003604 Andrew R. Booker, <a href="https://t5k.org/nthprime/">The Nth Prime Page</a>
%H A003604 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
%H A003604 R. G. Wilson v, <a href="/A006990/a006990.pdf">Letter to N. J. A. Sloane, Oct. 1993</a>
%H A003604 R. G. Wilson, V, <a href="/A007376/a007376.pdf">Letter to N. J. A. Sloane, Oct. 1993</a>
%H A003604 R. G. Wilson v, <a href="/A007014/a007014.pdf">Letter to N. J. A. Sloane, Jan. 1994</a>
%H A003604 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%t A003604 Table[PrimePi[n!], {n, 0, 16}]
%o A003604 (PARI) for(n=0,10,print(omega(n!!)))
%o A003604 (PARI) a(n)=primepi(n!) \\ _Charles R Greathouse IV_, Jan 21 2016
%o A003604 (Sage) [prime_pi(factorial(n)) for n in range(0, 14)] # _Zerinvary Lajos_, Jun 06 2009
%Y A003604 Cf. A000040, A000197.
%K A003604 hard,nonn
%O A003604 0,4
%A A003604 _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_
%E A003604 a(15) from _Jud McCranie_
%E A003604 a(16)-a(17) from _Paul Zimmermann_
%E A003604 a(18) from _Donovan Johnson_, Dec 18 2009
%E A003604 a(19) from _Donovan Johnson_, Feb 18 2010
%E A003604 a(20) from _Henri Lifchitz_, Nov 11 2012
%E A003604 a(21)-a(23) from _Henri Lifchitz_, Aug 26 2014