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%I #10 Aug 09 2015 15:37:12
%S 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,
%T 16,17,1,34,2,19,1,38,2,21,3,10,5,6,11,1,47,1,49,4,24,12,13,1,55,2,27,
%U 14,5,8,29,1,63,6,16,31,1,68,3,17,4,33,3,19,3,20,9,21,7,8,35,9,23,1,85,5,12
%N 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 If a(n-1) = 1, then a(n) = n-1, obviously.
%e 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 a(7)=3 and a(13) = 12 are the two terms each divisible by 3, so a(14) = 2.
%p 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_, Sep 06 2007
%Y Cf. A118290.
%K nonn
%O 1,3
%A _Leroy Quet_, Apr 22 2006
%E More terms from _R. J. Mathar_, Sep 06 2007