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A349617 Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation) with A055615 (Dirichlet inverse of n).

%I A349617 #13 Jan 27 2024 17:05:59
%S A349617 1,0,2,-1,5,-6,7,2,-9,-11,9,2,15,-15,-29,1,16,18,18,5,-41,-21,20,-4,
%T A349617 -26,-29,4,7,28,64,30,-3,-61,-34,-80,9,30,-38,-81,-6,33,92,38,14,51,
%U A349617 -44,42,10,-48,53,-99,6,47,4,-102,-17,-111,-58,48,-4,54,-62,69,2,-151,146,61,18,-131,157,63,-3,65,-68,92,18
%N A349617 Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation) with A055615 (Dirichlet inverse of n).
%C A349617 Dirichlet convolution of this sequence with A000010 (Euler phi) is A304526 (Möbius transform of the inverse permutation of EKG-sequence).
%H A349617 Antti Karttunen, <a href="/A349617/b349617.txt">Table of n, a(n) for n = 1..20000</a>
%H A349617 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%F A349617 a(n) = Sum_{d|n} A064664(d) * A055615(n/d).
%o A349617 (PARI)
%o A349617 A055615(n) = (n*moebius(n));
%o A349617 v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ Data prepared with _Chai Wah Wu_'s Dec 08 2014 Python-program given in A064413.
%o A349617 A064413(n) = v064413[n];
%o A349617 \\ Then its inverse A064664 is prepared:
%o A349617 m064664 = Map();
%o A349617 for(n=1,65539,mapput(m064664,A064413(n),n));
%o A349617 A064664(n) = mapget(m064664,n);
%o A349617 A349617(n) = sumdiv(n,d,A064664(d)*A055615(n/d));
%Y A349617 Cf. A055615, A064413, A064664, A349616 (Dirichlet inverse).
%Y A349617 Cf. also A000010, A304526, A349614.
%K A349617 sign,look
%O A349617 1,3
%A A349617 _Antti Karttunen_, Nov 23 2021