A073458 a(n) = floor(prime(n)/composite(n)).

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4

Offset: 1

Author

Labos Elemer, Aug 02 2002

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002808, A073459.

Programs

Maple

nextcomp:= proc(x) if isprime(x+1) then x+2 else x+1 fi end proc:
p:= 2; c:= 4: A[1]:= 0:
for n from 2 to 200 do
  p:= nextprime(p); c:= nextcomp(c);
  A[n]:= floor(p/c);
od:
seq(A[i],i=1..200); # Robert Israel, Sep 28 2016

Mathematica

Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];
a[n_] := Floor[Prime[n]/Composite[n]];
Array[a, 100] (* Jean-François Alcover, Jun 09 2020, after Robert G. Wilson v in A002808 *)
Module[{nn=200,cmps},cmps=Select[Range[nn],CompositeQ];Floor[#[[1]]/ #[[2]]]&/@ Thread[{Prime[Range[Length[cmps]]],cmps}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 21 2020 *)

Formula

a(n) = floor(A000040(n)/A002808(n)).