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A346237 Dirichlet inverse of A005187.

%I A346237 #11 Aug 13 2021 22:48:12
%S A346237 1,-3,-4,2,-8,14,-11,0,0,30,-19,-14,-23,41,38,0,-32,-2,-35,-34,49,73,
%T A346237 -42,4,17,89,14,-46,-54,-172,-57,0,88,126,109,10,-71,137,110,12,-79,
%U A346237 -219,-82,-86,-6,164,-89,0,26,-103,158,-106,-102,-76,199,16,170,212,-113,274,-117,223,16,0,240,-406,-131,-154,201
%N A346237 Dirichlet inverse of A005187.
%H A346237 Antti Karttunen, <a href="/A346237/b346237.txt">Table of n, a(n) for n = 1..16384</a>
%F A346237 a(n) = A346238(n) - A005187(n).
%o A346237 (PARI)
%o A346237 up_to = 65537;
%o A346237 DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A346237 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A346237 v346237 = DirInverseCorrect(vector(up_to,n,A005187(n)));
%o A346237 A346237(n) = v346237[n];
%Y A346237 Cf. A005187, A346238.
%Y A346237 Cf. also A297111, A317927, A317928.
%K A346237 sign
%O A346237 1,2
%A A346237 _Antti Karttunen_, Jul 13 2021