cp's OEIS Frontend

A346479 Dirichlet inverse of A250469.

%I A346479 #13 Oct 29 2021 12:26:16
%S A346479 1,-3,-5,0,-7,15,-11,6,0,15,-13,12,-17,27,35,0,-19,24,-23,42,55,15,
%T A346479 -29,-66,0,27,60,54,-31,-27,-37,-12,45,15,77,-144,-41,27,75,-102,-43,
%U A346479 -63,-47,132,60,39,-53,-24,0,84,65,144,-59,-384,91,-162,85,15,-61,-558,-67,39,120,0,119,165,-71,222,115,9,-73,168
%N A346479 Dirichlet inverse of A250469.
%C A346479 Not all zeros occur on squares. For example, a(1445) = a(5 * 17^2) = 0.
%H A346479 Antti Karttunen, <a href="/A346479/b346479.txt">Table of n, a(n) for n = 1..10000</a>
%H A346479 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A346479 a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, d<n} a(d) * A250469(n/d).
%F A346479 a(n) = A346480(n) - A250469(n).
%o A346479 (PARI)
%o A346479 up_to = 16384;
%o A346479 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 A346479 v346479 = DirInverseCorrect(vector(up_to,n,A250469(n)));
%o A346479 A346479(n) = v346479[n];
%Y A346479 Cf. A250469, A346480.
%Y A346479 Cf. also A346234, A346477.
%K A346479 sign
%O A346479 1,2
%A A346479 _Antti Karttunen_, Jul 30 2021