%I A118291
%S A118291 1,1,2,1,4,2,3,1,8,4,5,1,12,2,7,1,16,8,9,3,4,10,2,12,5,3,6,7,2,15,4,16,
%T A118291 17,1,34,2,19,1,38,2,21,3,10,5,6,11,1,47,1,49,4,24,12,13,1,55,2,27,14,
               5,
%U A118291 8,29,1,63,6,16,31,1,68,3,17,4,33,3,19,3,20,9,21,7,8,35,9,23,1,85,5,12
%N A118291 a(1) = 1. a(n) = number of terms among the sequence's first (n-1) terms 
               which are divisible by the largest prime dividing a(n-1), or which 
               are divisible by 1 if a(n-1)= 1.
%C A118291 If a(n-1) = 1, then a(n) = n-1, obviously.
%H A118291 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A118291 a(13)= 12. So a(14) = the number of terms among the first 13 terms which 
               are divisible by the largest prime dividing 12 (which is 3).
%e A118291 a(7)=3 and a(13) = 12 are the two terms each divisible by 3, so a(14) 
               = 2.
%p A118291 A006530 := proc(n) local ifs,i ; if n <= 3 then n ; else ifs := ifactors(n)[2] 
               ; max( seq(op(1,i),i=ifs)) ; fi ; end: A118291 := proc(n) local a,
               anxt,i ; a := [1,1] ; while nops(a) < n do anxt := 0 ; for i in a 
               do if i mod A006530(op(-1,a)) = 0 then anxt := anxt+1 ; fi ; od: 
               a := [op(a),anxt] ; od; a ; end: A118291(200) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 06 2007
%Y A118291 Cf. A118290.
%Y A118291 Sequence in context: A007733 A128520 A123755 this_sequence A118290 A132223 
               A135941
%Y A118291 Adjacent sequences: A118288 A118289 A118290 this_sequence A118292 A118293 
               A118294
%K A118291 nonn
%O A118291 1,3
%A A118291 Leroy Quet Apr 22 2006
%E A118291 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 06 2007