%I A160102
%S A160102 1,2,3,5,7,6,11,10,13,14,17,15,19,22,21,23,29,26,31,35,33,34,37,30,41,
%T A160102 38,39,55,43,42,47,46,51,58,77,65,53,62,57,70,59,66,61,85,91,74,67,69,
%U A160102 71,82,87,95,73,78,119,110,93,86,79,105,83,94,143,115,133,102,89,145
%N A160102 Multiplicative function, one-to-one and onto the square-free numbers.
%C A160102 Multiplicative with a(A050376(k)) = Prime(k) = A000040(k). If k = 2^{i_1} 
               + ... + 2^{i_j} is the binary representation of k, a(p^k) = a(p^2^{i_1}) 
               * ... * a(p^2^{i_j}).
%o A160102 (PARI) al(n)={local(v,k,fm,m,p);
%o A160102 v=vector(n);v[1]=1;p=1;
%o A160102 for(k=2,n,fm=factor(k);
%o A160102 if(matsize(fm)[1]>1,m=fm[1,1]^fm[1,2];v[k]=v[m]*v[k/m],
%o A160102 m=2^valuation(fm[1,2],2);
%o A160102 if(m==fm[1,2],p=nextprime(p+1);v[k]=p,
%o A160102 m=fm[1,1]^m;v[k]=v[m]*v[k/m])));
%o A160102 v}
%Y A160102 Cf. A005117, A050376, A000040.
%Y A160102 Sequence in context: A126890 A122637 A076229 this_sequence A137750 A156900 
               A039734
%Y A160102 Adjacent sequences: A160099 A160100 A160101 this_sequence A160103 A160104 
               A160105
%K A160102 mult,nonn
%O A160102 1,2
%A A160102 Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 01 2009