cp's OEIS Frontend

A323913 Sum of A083254 (2*phi(n) - n) and its Dirichlet inverse.

%I A323913 #6 Feb 12 2019 22:37:35
%S A323913 2,0,0,0,0,0,0,0,1,0,0,0,0,0,6,0,0,-4,0,0,10,0,0,0,9,0,5,0,0,-16,0,0,
%T A323913 18,0,30,-4,0,0,22,0,0,-24,0,0,11,0,0,0,25,-12,30,0,0,-18,54,0,34,0,0,
%U A323913 -24,0,0,21,0,66,-40,0,0,42,-32,0,0,0,0,9,0,90,-48,0,0,19,0,0,-40,90,0,54,0,0,-38,110,0,58,0,102,0,0,-20
%N A323913 Sum of A083254 (2*phi(n) - n) and its Dirichlet inverse.
%H A323913 Antti Karttunen, <a href="/A323913/b323913.txt">Table of n, a(n) for n = 1..20000</a>
%o A323913 (PARI)
%o A323913 up_to = 16384;
%o A323913 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 A323913 A083254(n) = (2*eulerphi(n)-n);
%o A323913 v323912 = DirInverse(vector(up_to,n,A083254(n)));
%o A323913 A323912(n) = v323912[n];
%o A323913 A323913(n) = (A083254(n)+A323912(n));
%Y A323913 Cf. A000010, A083254, A319340, A323911, A323912.
%K A323913 sign
%O A323913 1,1
%A A323913 _Antti Karttunen_, Feb 12 2019