login
a(0)=1; for n>0, a(n) = number of earlier terms of the sequence that divide the n-th composite positive integer.
1

%I #11 Aug 12 2015 21:10:44

%S 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,

%T 4,23,5,7,8,10,13,5,17,8,4,26,4,13,17,8,13,13,9,13,29,4,12,12,7,19,24,

%U 10,4,30,7,4,9,21,23,14,16,8,4,6,38,11,13,21,15,30,21,4,32,12,8,33,15,7,17

%N a(0)=1; for n>0, a(n) = number of earlier terms of the sequence that divide the n-th composite positive integer.

%e The 7th composite is 14. There are three terms from among (a(0),a(1),...a(6)) that divide 14 (a(0)=1, a(1)=1, a(2)=2). So a(7) = 3.

%p 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_, May 27 2007

%p 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_, Jun 08 2007

%K nonn

%O 0,3

%A _Leroy Quet_, May 13 2007

%E More terms from _Emeric Deutsch_ and _R. J. Mathar_, May 27 2007