cp's OEIS Frontend

A305807 Dirichlet inverse of A032742 (the largest proper divisor of n).

%I A305807 #11 Feb 17 2020 07:37:13
%S A305807 1,-1,-1,-1,-1,-1,-1,-1,-2,-3,-1,1,-1,-5,-3,-1,-1,0,-1,1,-5,-9,-1,3,
%T A305807 -4,-11,-4,1,-1,5,-1,-1,-9,-15,-5,6,-1,-17,-11,5,-1,7,-1,1,-2,-21,-1,
%U A305807 5,-6,-8,-15,1,-1,4,-9,7,-17,-27,-1,19,-1,-29,-4,-1,-11,11,-1,1,-21,-3,-1,8,-1,-35,-8,1,-9,13,-1,9,-8,-39,-1,29,-15,-41,-27,11,-1
%N A305807 Dirichlet inverse of A032742 (the largest proper divisor of n).
%H A305807 Antti Karttunen, <a href="/A305807/b305807.txt">Table of n, a(n) for n = 1..65537</a>
%F A305807 a(1) = 1; for n > 1, a(n) = -Sum_{d|n, d<n} A032742(n/d)*a(d).
%t A305807 b[n_] := If[n == 1, 1, Divisors[n][[-2]]];
%t A305807 a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@ Divisors[n]}]];
%t A305807 Array[a, 100] (* _Jean-François Alcover_, Feb 17 2020 *)
%o A305807 (PARI)
%o A305807 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A305807 A305807(n) = if(1==n,1,-sumdiv(n,d,if(d<n,A032742(n/d)*A305807(d),0)));
%Y A305807 Cf. A032742, A300236, A300239, A305808.
%K A305807 sign
%O A305807 1,9
%A A305807 _Antti Karttunen_, Jun 13 2018