cp's OEIS Frontend

A340145 Dirichlet inverse of A247074(x) = phi(x)/(Product_{primes p dividing x} gcd(p-1, x-1)).

%I A340145 #6 Dec 30 2020 20:00:08
%S A340145 1,-1,-1,-1,-1,0,-1,-1,-2,-2,-1,1,-1,-4,0,-1,-1,1,-1,1,-1,-8,-1,2,-4,
%T A340145 -10,-4,9,-1,2,-1,-1,-3,-14,-4,3,-1,-16,-4,4,-1,4,-1,1,4,-20,-1,3,-6,
%U A340145 -5,-6,17,-1,4,-8,-10,-7,-26,-1,6,-1,-28,0,-1,-1,24,-1,1,-9,18,-1,4,-1,-34,1,25,-13,10,-1,7,-8,-38,-1
%N A340145 Dirichlet inverse of A247074(x) = phi(x)/(Product_{primes p dividing x} gcd(p-1, x-1)).
%H A340145 Antti Karttunen, <a href="/A340145/b340145.txt">Table of n, a(n) for n = 1..8191</a>
%H A340145 Antti Karttunen, <a href="/A340145/a340145.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A340145 (PARI)
%o A340145 up_to = 65537;
%o A340145 A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
%o A340145 DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -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 A340145 v340145 = DirInverse(vector(up_to, n, A247074(n)));
%o A340145 A340145(n) = v340145[n];
%Y A340145 Cf. A247074.
%Y A340145 Cf. also A340142, A340144, A340146.
%K A340145 sign
%O A340145 1,9
%A A340145 _Antti Karttunen_, Dec 29 2020