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A160102 Multiplicative function, one-to-one and onto the squarefree numbers. 1

%I

%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(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}).

%H Ivan Neretin, <a href="/A160102/b160102.txt">Table of n, a(n) for n = 1..10000</a>

%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 Cf. A005117, A050376, A000040.

%K mult,nonn

%O 1,2

%A _Franklin T. Adams-Watters_, May 01 2009

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Last modified October 18 18:22 EDT 2019. Contains 328187 sequences. (Running on oeis4.)