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.
%I A129309 #12 May 17 2017 03:16:48 %S A129309 1,1,3,3,2,3,4,4,5,5,6,6,6,7,8,7,8,7,7,10,9,9,9,9,10,10,10,10,12,12, %T A129309 12,13,14,13,13,13,14,14,14,14,14,14,16,16,17,16,15,17,17,16,18,19,19, %U A129309 19,19,18,20,21,20,20,21,21,21,21,21,22,22,22,22,22,22,23,23,23,23,25,24 %N A129309 a(n) = number of primes which are < c(n) and are coprime to c(n), where c(n) is the n-th composite. %H A129309 G. C. Greubel, <a href="/A129309/b129309.txt">Table of n, a(n) for n = 1..10000</a> %F A129309 a(n) = A048865(A002808(n)) = A000720(A002808(n)) - A001221(A002808(n)). %p A129309 A002808 := proc(n) local resul,i ; i := 1 ; resul := 4 ; while i < n do resul := resul+1 ; while isprime(resul) do resul := resul+1 ; od ; i := i+1 ; od; RETURN(resul) ; end: A000720 := proc(n) numtheory[pi](n) ; end: A001221 := proc(n) nops(numtheory[factorset](n)) ; end: A048865 := proc(n) A000720(n)-A001221(n) ; end: A129309 := proc(n) A048865(A002808(n)) ; end: seq(A129309(n),n=1..80) ; # _R. J. Mathar_, Jun 15 2007 %t A129309 A002808[n_] := Select[Range[2, 2*n], ! PrimeQ[#] &]; A048865[n_] := PrimePi[n] - PrimeNu[n]; A048865[A002808[50]] (* _G. C. Greubel_, May 16 2017 *) %Y A129309 Cf. A048865. %K A129309 nonn %O A129309 1,3 %A A129309 _Leroy Quet_, May 26 2007 %E A129309 More terms from _R. J. Mathar_, Jun 15 2007