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A294649 a(n) = numerator(A206369(n))/n.

%I A294649 #14 Dec 23 2017 04:49:18
%S A294649 1,1,2,3,4,1,6,5,7,2,10,1,12,3,8,11,16,7,18,3,4,5,22,5,21,6,20,9,28,4,
%T A294649 30,21,20,8,24,7,36,9,8,1,40,2,42,15,28,11,46,11,43,21,32,9,52,10,8,
%U A294649 15,12,14,58,2,60,15,2,43,48,10,66,12,44,12,70,35,72,18,14
%N A294649 a(n) = numerator(A206369(n))/n.
%C A294649 a(n) = 1 for n in A127724.
%H A294649 Michel Marcus, <a href="/A294649/b294649.txt">Table of n, a(n) for n = 1..10000</a>
%H A294649 László Tóth, <a href="http://arxiv.org/abs/1111.4842">A survey of the alternating sum-of-divisors function</a>, arXiv:1111.4842 [math.NT], 2011-2014.
%t A294649 (* b = A209369 *) b[n_] := n*DivisorSum[n, LiouvilleLambda[#]/# &];
%t A294649 a[n_] := Numerator[b[n]/n];
%t A294649 Array[a, 100] (* _Jean-François Alcover_, Dec 04 2017 *)
%o A294649 (PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
%o A294649 rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
%o A294649 a(n) = numerator(rho(n)/n);
%Y A294649 Cf. A127724 (k-imperfect), A206369, A294650 (denominator).
%Y A294649 A225679 is a subsequence (on squarefree indices). - _Michel Marcus_, Dec 22 2017
%K A294649 nonn,frac
%O A294649 1,3
%A A294649 _Michel Marcus_, Nov 06 2017