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%I #11 Mar 31 2017 20:56:57
%S 1,2,3,2,2,5,6,7,2,2,2,3,3,10,11,6,2,13,14,15,2,2,2,2,17,6,3,19,10,2,
%T 21,22,23,6,2,2,5,5,26,3,3,3,14,2,29,30,31,2,2,2,2,2,33,34,35,6,6,37,
%U 38,39,10,2,2,41,42,43,22,2,15,3,46,47,6,2,2,2,7,7,10,5,51,26,2,53,6,3,3,55
%N In the sequence of natural numbers, replace the nonsquarefree numbers with their minimal factorization into squarefree numbers.
%C a(A129132(n-1) + 2) = A007947(n) for n > 1. - _Reinhard Zumkeller_, Mar 30 2007
%H R. Zumkeller, <a href="/A128651/b128651.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F a(n) = f(n,1,2,2,1) with f(n,m,x,y,z) = if n=m then z else if rad(y)=y then f(n,m+1,x+1,x+1,y) else f(n,m+1,x,y/rad(y),rad(y)), rad = squarefree kernel (A007947).
%e 1 2 3 _ 4 5 6 7 _ _ 8 _ 9 10 11 _12 13 14 15 _ _ _16 ....
%e 1 2 3 2 2 5 6 7 2 2 2 3 3 10 11 6 2 13 14 15 2 2 2 2 ....
%Y Cf. A013929, A007947, A003557.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Mar 18 2007
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