%I A126854
%S A126854 1,1,2,3,3,3,6,3,6,3,10,4,7,3,12,2,4,8,7,13,7,8,4,5,16,4,9,12,15,8,11,
               4,
%T A126854 23,5,7,8,10,13,5,17,8,4,26,4,13,17,8,13,13,9,13,29,4,12,12,7,19,24,10,
%U A126854 4,30,7,4,9,21,23,14,16,8,4,6,38,11,13,21,15,30,21,4,32,12,8,33,15,7,17
%N A126854 a(0)=1; for n>0, a(n) = number of earlier terms of the sequence which 
               divide the n-th composite positive integer.
%H A126854 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A126854 The 7th composite is 14. There are three terms from among (a(0),a(1),
               ...a(6)) which divide 14 (a(0)=1, a(1)=1, a(2)=2). So a(7) = 3.
%p A126854 c:=proc(n) if isprime(n)=false then n else fi end: C:=[seq(c(n),n=2..200)]: 
               a[0]:=1: for n from 1 to 110 do a[n]:=0: for j from 0 to n-1 do if 
               C[n] mod a[j] = 0 then a[n]:=a[n]+1 else fi od: od: seq(a[n],n=0..110); 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 27 2007
%p A126854 A002805 := proc(n) option remember ; local a; if n = 1 then 4 ; else 
               a := 1+A002805(n-1) ; while isprime(a) do a := a+1 ; od ; RETURN(a) 
               ; fi ; end: A126854 := proc(nmax) local a,anext,n,acomp,i; a := [1] 
               ; while nops(a) < nmax do n := nops(a) ; anext := 0 ; acomp := A002805(n) 
               ; for i from 1 to n do if acomp mod op(i,a) = 0 then anext := anext+1 
               ; fi ; od ; a := [op(a),anext] ; od ; a ; end: A126854(100) ; - R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2007
%Y A126854 Sequence in context: A078644 A133700 A087688 this_sequence A115206 A093653 
               A049982
%Y A126854 Adjacent sequences: A126851 A126852 A126853 this_sequence A126855 A126856 
               A126857
%K A126854 nonn
%O A126854 0,3
%A A126854 Leroy Quet May 13 2007
%E A126854 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), May 27 2007