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a(n) = floor(prime(n)/composite(n)).
2

%I #15 Dec 21 2020 12:38:44

%S 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,

%T 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,

%U 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

%N a(n) = floor(prime(n)/composite(n)).

%H Robert Israel, <a href="/A073458/b073458.txt">Table of n, a(n) for n = 1..10000</a>

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

%p nextcomp:= proc(x) if isprime(x+1) then x+2 else x+1 fi end proc:

%p p:= 2; c:= 4: A[1]:= 0:

%p for n from 2 to 200 do

%p p:= nextprime(p); c:= nextcomp(c);

%p A[n]:= floor(p/c);

%p od:

%p seq(A[i],i=1..200); # _Robert Israel_, Sep 28 2016

%t Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];

%t a[n_] := Floor[Prime[n]/Composite[n]];

%t Array[a, 100] (* _Jean-François Alcover_, Jun 09 2020, after _Robert G. Wilson v_ in A002808 *)

%t 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 *)

%Y Cf. A000040, A002808, A073459.

%K nonn

%O 1,16

%A _Labos Elemer_, Aug 02 2002