cp's OEIS Frontend

A346482 Dirichlet inverse of A005171, the characteristic function of nonprimes.

%I A346482 #14 Nov 14 2021 00:49:00
%S A346482 1,0,0,-1,0,-1,0,-1,-1,-1,0,-1,0,-1,-1,0,0,-1,0,-1,-1,-1,0,1,-1,-1,-1,
%T A346482 -1,0,-1,0,1,-1,-1,-1,2,0,-1,-1,1,0,-1,0,-1,-1,-1,0,3,-1,-1,-1,-1,0,1,
%U A346482 -1,1,-1,-1,0,3,0,-1,-1,1,-1,-1,0,-1,-1,-1,0,5,0,-1,-1,-1,-1,-1,0,3,0,-1,0,3,-1,-1,-1,1,0,3
%N A346482 Dirichlet inverse of A005171, the characteristic function of nonprimes.
%C A346482 In addition to A168645, -1's occur also in the following positions: 256, 512, 6561, 16384, 19683, 32768, 390625, 1048576, ...
%H A346482 Antti Karttunen, <a href="/A346482/b346482.txt">Table of n, a(n) for n = 1..20000</a>
%F A346482 a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, d<n} a(d) * A005171(n/d).
%F A346482 a(n) = A346483(n) - A005171(n).
%o A346482 (PARI)
%o A346482 up_to = 65537;
%o A346482 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 A346482 A005171(n) = (1-isprime(n));
%o A346482 v346482 = DirInverseCorrect(vector(up_to,n,A005171(n)));
%o A346482 A346482(n) = v346482[n];
%Y A346482 Cf. A005171, A010051, A018252, A168645, A346483.
%Y A346482 Union of A000040 and A346484 gives the positions of zeros.
%K A346482 sign
%O A346482 1,36
%A A346482 _Mats Granvik_ and _Antti Karttunen_, Aug 17 2021