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%I #9 Apr 09 2014 10:14:03
%S 1,1,2,3,4,3,6,7,8,7,10,7,12,7,9,15,16,13,18,15,10,16,22,16,24,18,26,
%T 21,28,14,30,31,22,22,22,29,36,24,26,31,40,14,42,35,33,29,46,32,48,32,
%U 37,44,52,36,41,41,43,38,58,36,60,40,46,63,51,32,66,57,49,35,70,59,72
%N a(1)=1. a(n) = number of this sequence's terms a(m), 1<= m <= n-1, each with b(a(m),p) not equal to each b(n,p) for every prime p dividing n, where p^b(k,p) is the highest power of the prime p to divide k.
%H Owen Whitby, <a href="/A116991/b116991.txt">Table of n, a(n) for n = 1..500</a>
%e Among the sequence's first 11 terms there are 7 terms that share no common prime-power in their prime-factorization with the prime-powers in the prime-factorization of 12. 12 = 2^2 *3^1. The 7 terms sharing no prime-power with 12 are 1, 1, 2, 7, 8, 7 and 10. The other 4 terms (3, 4, 3 and 6) each share at least one prime-power with 12 in the integers' prime-factorizations.
%t alist={1};flist={{{1,1}}};Do[a=Length[Select[flist,Intersection[ #,FactorInteger[n]]=={}&]];AppendTo[alist,a];AppendTo[flist,FactorInteger[a]],{n,2,500}];Print[alist] - _Owen Whitby_, May 20 2008
%K nonn
%O 1,3
%A _Leroy Quet_, Apr 02 2006
%E More terms from _Owen Whitby_, May 20 2008
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