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%I #66 Sep 30 2020 03:52:56
%S 0,1,3,10,46,343,3248,42331,646029,12283531,300369796,8028643010,
%T 259488750744,9414916809095,362597750396740,15397728527812858,
%U 742238179058722891,40068968501510691894,2251262473052300960826,139566579945945392719413
%N Number of primes <= product of first n primes, A002110(n).
%H David Baugh, <a href="/A000849/b000849.txt">Table of n, a(n) for n = 0..19</a> (terms n = 18..19 found using Kim Walisch's primecount program).
%H R. Mestrovic, <a href="http://arxiv.org/abs/1211.4571">An elementary proof of an estimate for a number of primes less than the product of the first n primes</a>, arXiv:1211.4571 [math.NT], 2012.
%H C. D. Pruitt, <a href="http://web.archive.org/web/20120117034148/http://mathematical.com/mathprimorialproof.html">A Theorem & Proof on the Density of Primes Utilizing Primorials</a>
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
%F a(n) = A000720(A002110(n)). - _Michel Marcus_, Aug 25 2014
%p seq(numtheory:-pi(mul(ithprime(i),i=1..n)),n=0..10); # _Robert Israel_, Aug 25 2014
%t a=1; Table[a=a*Prime[n]; PrimePi[a], {n, 12}]
%t Join[{0},PrimePi/@FoldList[Times,Prime[Range[12]]]] (* _Harvey P. Dale_, Jan 28 2019 *)
%o (PARI) t=1;forprime(p=2,66,print1(primepi(t),", ");t*=p); \\ _Joerg Arndt_, Aug 25 2014
%o (Sage) [prime_pi(sloane.A002110(n)) for n in range (14)] # _Giuseppe Coppoletta_, Mar 02 2015
%Y Cf. A000720, A002110, A003604.
%K nonn,hard
%O 0,3
%A James D. Ausfahl, gandalf(AT)hrn.office.ssi.net
%E More terms from _David W. Wilson_
%E a(10)-a(13) from _Paul Zimmermann_
%E a(14)-a(15) from _Donovan Johnson_, Mar 01 2010
%E a(16)-a(17) from _Henri Lifchitz_, Aug 25 2014
%E a(18)-a(19) from _David Baugh_, Sep 29 2020