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A318665 Denominators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.

%I A318665 #6 Sep 01 2018 22:28:26
%S A318665 1,1,2,1,1,2,1,1,8,2,1,2,1,2,1,1,2,8,2,2,1,2,2,2,2,2,16,2,2,4,2,2,2,2,
%T A318665 2,8,2,2,2,1,1,4,2,1,8,2,2,2,2,1,4,1,1,16,2,2,4,2,2,4,2,2,8,1,1,4,1,2,
%U A318665 4,1,1,8,1,2,4,2,1,4,2,1,128,2,1,4,2,2,4,1,2,16,2,2,4,2,1,4,1,1,2,8,2,4,2,2,4
%N A318665 Denominators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.
%H A318665 Antti Karttunen, <a href="/A318665/b318665.txt">Table of n, a(n) for n = 1..16384</a>
%H A318665 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%F A318665 a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A064664(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o A318665 (PARI)
%o A318665 v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared previously.
%o A318665 A064413(n) = v064413[n];
%o A318665 m064664 = Map();
%o A318665 for(n=1,65539,mapput(m064664,A064413(n),n));
%o A318665 A064664(n) = mapget(m064664,n);
%o A318665 up_to = (2^14);
%o A318665 DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
%o A318665 v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));
%o A318665 A318664(n) = numerator(v318664_65[n]);
%o A318665 A318665(n) = denominator(v318664_65[n]);
%Y A318665 Cf. A064664, A304526, A304527, A318664 (numerators).
%K A318665 nonn,frac
%O A318665 1,3
%A A318665 _Antti Karttunen_, Sep 01 2018