cp's OEIS Frontend

A342417 Dirichlet inverse of Čiurlionis sequence, A342002.

%I A342417 #14 Jan 02 2023 16:49:34
%S A342417 1,-1,-5,-1,-7,9,-7,-5,-6,1,-41,5,-9,3,33,-1,-47,-6,-11,19,27,63,-53,
%T A342417 41,36,1,136,7,-59,7,-9,25,369,77,43,16,-59,-49,-157,-9,-317,-19,-73,
%U A342417 -13,-10,-21,-359,-53,-38,-52,139,-105,-401,-348,473,-23,-263,-51,-443,-201,-11,5,292,23,65,-893,-69,-5,253,31
%N A342417 Dirichlet inverse of Čiurlionis sequence, A342002.
%H A342417 Antti Karttunen, <a href="/A342417/b342417.txt">Table of n, a(n) for n = 1..11550</a>
%o A342417 (PARI)
%o A342417 up_to = 11550;
%o A342417 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 A342417 A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
%o A342417 v342417 = DirInverseCorrect(vector(up_to,n,A342002(n)));
%o A342417 A342417(n) = v342417[n];
%Y A342417 Cf. A342002, A342419.
%Y A342417 Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).
%Y A342417 Cf. also A359427.
%K A342417 sign
%O A342417 1,3
%A A342417 _Antti Karttunen_, Mar 13 2021