cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071903 Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e., in A004614).

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%I A071903 #19 Jul 31 2017 03:26:46
%S A071903 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 A071903 11,11,11,11,11,11,11,11,11,12,12,12,12,13,13,14,14,14,14,14,14,14,14,
%U A071903 15,15,16,16,16,16,17,17,17,17,18,18,19,19,20,20,20,20,20,20,21,21,22
%N A071903 Number of x less than or equal to n and divisible only by primes congruent to 3 mod 4 (i.e., in A004614).
%D A071903 Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669.
%H A071903 Michael De Vlieger, <a href="/A071903/b071903.txt">Table of n, a(n) for n = 0..10000</a>
%H A071903 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 A071903 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 A071903 a(n) = Card{ k | A004614(k) <= n }.
%F A071903 Asymptotically: a(n) ~ sqrt(2)*A*n/(Pi*sqrt(log(n))) where A = Product_{k>0} ((1-A002145(k)^(-2))^(-1/2)).
%t A071903 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 A071903 (PARI) for(n=1,100,print1(sum(i=1,n,if(sumdiv(i,d,isprime(d)*(d-3)%4),0,1)),","))
%Y A071903 Cf. A002145, A004614.
%K A071903 easy,nonn
%O A071903 0,3
%A A071903 _Benoit Cloitre_, Jun 12 2002