A129309 a(n) = number of primes which are < c(n) and are coprime to c(n), where c(n) is the n-th composite.

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, 12, 13, 14, 13, 13, 13, 14, 14, 14, 14, 14, 14, 16, 16, 17, 16, 15, 17, 17, 16, 18, 19, 19, 19, 19, 18, 20, 21, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 25, 24

Offset: 1

Author

Leroy Quet, May 26 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048865.

Programs

Maple

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

Mathematica

A002808[n_] := Select[Range[2, 2*n], ! PrimeQ[#] &]; A048865[n_] := PrimePi[n] - PrimeNu[n]; A048865[A002808[50]] (* G. C. Greubel, May 16 2017 *)

Formula

a(n) = A048865(A002808(n)) = A000720(A002808(n)) - A001221(A002808(n)).

Extensions

More terms from R. J. Mathar, Jun 15 2007