cp's OEIS Frontend

A349614 Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation, A064413) with the Dirichlet inverse of A064413.

%I A349614 #9 Nov 25 2021 20:01:52
%S A349614 1,0,1,-3,7,-7,2,6,-8,-10,5,9,14,2,-41,-1,17,27,15,-6,-38,-18,13,10,
%T A349614 -32,-29,18,33,18,62,29,-13,-31,-53,-107,25,48,-51,-86,13,30,116,58,
%U A349614 23,88,-34,37,-47,-30,56,-113,3,45,-39,-137,-154,-73,-67,41,160,84,-91,174,56,-154,152,91,6,-113,246,58,-185,56
%N A349614 Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation, A064413) with the Dirichlet inverse of A064413.
%C A349614 Obviously, convolving this with A064413 gives its inverse permutation A064664.
%H A349614 Antti Karttunen, <a href="/A349614/b349614.txt">Table of n, a(n) for n = 1..20000</a>
%H A349614 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%F A349614 a(n) = Sum_{d|n} A064664(d) * A349400(n/d).
%o A349614 (PARI)
%o A349614 up_to = 32768;
%o A349614 v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ Data prepared with _Chai Wah Wu_'s Dec 08 2014 Python-program given in A064413.
%o A349614 A064413(n) = v064413[n];
%o A349614 \\ Then its inverse A064664 is prepared:
%o A349614 m064664 = Map();
%o A349614 for(n=1,65539,mapput(m064664,A064413(n),n));
%o A349614 A064664(n) = mapget(m064664,n);
%o A349614 memoA349400 = Map();
%o A349614 A349400(n) = if(1==n,1,my(v); if(mapisdefined(memoA349400,n,&v), v, v = -sumdiv(n,d,if(d<n,A064413(n/d)*A349400(d),0)); mapput(memoA349400,n,v); (v)));
%o A349614 A349614(n) = sumdiv(n,d,A064664(d)*A349400(n/d));
%Y A349614 Cf. A064413, A064664, A349400, A349613 (Dirichlet inverse), A349615 (sum with it), A349617.
%Y A349614 Cf. also pairs A349376, A349377 and A349397, A349398 for similar constructions.
%K A349614 sign
%O A349614 1,4
%A A349614 _Antti Karttunen_, Nov 23 2021