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%I #19 Jul 31 2017 03:26:46
%S 1,1,2,2,2,2,3,3,4,4,5,5,5,5,5,5,5,5,6,6,7,7,8,8,8,8,9,9,9,9,10,10,11,
%T 11,11,11,11,11,11,11,11,11,12,12,12,12,13,13,14,14,14,14,14,14,14,14,
%U 15,15,16,16,16,16,17,17,17,17,18,18,19,19,20,20,20,20,20,20,21,21,22
%N Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e., in A004614).
%D Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669.
%H Michael De Vlieger, <a href="/A071903/b071903.txt">Table of n, a(n) for n = 0..10000</a>
%H E. Landau, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;c=umhistmath;idno=ABV2766.0002.001">Handbuch der Lehre von der Verteilung der Primzahlen</a>, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
%H E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, <a href="http://name.umdl.umich.edu/ABV2766.0001.001">vol. 1</a> and <a href="http://name.umdl.umich.edu/ABV2766.0002.001">vol. 2</a>, Leipzig, Berlin, B. G. Teubner, 1909.
%F a(n) = Card{ k | A004614(k) <= n }.
%F Asymptotically: a(n) ~ sqrt(2)*A*n/(Pi*sqrt(log(n))) where A = Product_{k>0} ((1-A002145(k)^(-2))^(-1/2)).
%t With[{s = {1}~Join~Select[Range@ 80, AllTrue[FactorInteger[#][[All, 1]], Mod[#, 4] == 3 &] &]}, Table[LengthWhile[s, # <= n &], {n, Max@ s}]] (* _Michael De Vlieger_, Jul 30 2017 *)
%o (PARI) for(n=1,100,print1(sum(i=1,n,if(sumdiv(i,d,isprime(d)*(d-3)%4),0,1)),","))
%Y Cf. A002145, A004614.
%K easy,nonn
%O 0,3
%A _Benoit Cloitre_, Jun 12 2002
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