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%I #13 Jan 14 2020 01:08:36
%S 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 38,39,55,43,42,47,46,51,58,77,65,53,62,57,70,59,66,61,85,91,74,67,69,
%U 71,82,87,95,73,78,119,110,93,86,79,105,83,94,143,115,133,102,89,145
%N Multiplicative function, one-to-one and onto the squarefree numbers.
%C Multiplicative with a(A050376(m)) = Prime(m) = A000040(m). 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}). [edited by _Peter Munn_, Jan 07 2020]
%C Equivalently, a(A050376(m)) = A000040(m); a(A059897(n,k)) = A059897(a(n), a(k)). - _Peter Munn_, Dec 30 2019
%H Ivan Neretin, <a href="/A160102/b160102.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Peter Munn_, Dec 30 2019: (Start)
%F a(n) = A019565(A052331(n)).
%F a(A052330(k)) = A019565(k).
%F (End)
%o (PARI) al(n)={local(v,k,fm,m,p);
%o v=vector(n);v[1]=1;p=1;
%o for(k=2,n,fm=factor(k);
%o if(matsize(fm)[1]>1,m=fm[1,1]^fm[1,2];v[k]=v[m]*v[k/m],
%o m=2^valuation(fm[1,2],2);
%o if(m==fm[1,2],p=nextprime(p+1);v[k]=p,
%o m=fm[1,1]^m;v[k]=v[m]*v[k/m])));
%o v}
%Y Sequences used in definitions of this sequence: A000040, A019565, A050376, A052331, A059897.
%Y Cf. A005117 (range of values), A052330.
%K mult,nonn
%O 1,2
%A _Franklin T. Adams-Watters_, May 01 2009
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