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A305805 Dirichlet inverse of A175851.

%I A305805 #9 Feb 17 2020 07:36:34
%S A305805 1,-1,-1,-1,-1,0,-1,1,-2,-2,-1,3,-1,0,-1,-1,-1,5,-1,7,-1,-2,-1,0,-2,
%T A305805 -2,0,-1,-1,10,-1,3,-1,-2,-3,-3,-1,0,-1,0,-1,6,-1,7,6,-2,-1,-1,-2,7,
%U A305805 -3,3,-1,4,-1,6,-3,-4,-1,-7,-1,0,6,-1,-3,6,-1,7,-1,12,-1,-4,-1,0,6,1,-3,6,-1,-5,8,-2,-1,5,-1,-2,-3,-2,-1,0,-1,5
%N A305805 Dirichlet inverse of A175851.
%H A305805 Antti Karttunen, <a href="/A305805/b305805.txt">Table of n, a(n) for n = 1..65537</a>
%F A305805 a(1) = 1; for n > 1, a(n) = -Sum_{d|n, d<n} A175851(n/d)*a(d).
%t A305805 b[n_] := If[n < 3, 1, n - NextPrime[n + 1, -1] + 1];
%t A305805 a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@Divisors[n]}]];
%t A305805 Array[a, 100] (* _Jean-François Alcover_, Feb 17 2020 *)
%o A305805 (PARI)
%o A305805 A175851(n) = if(1==n,n,1 + n - precprime(n));
%o A305805 A305805(n) = if(1==n,1,-sumdiv(n,d,if(d<n,A175851(n/d)*A305805(d),0)));
%Y A305805 Cf. A175851, A305791, A305806.
%K A305805 sign
%O A305805 1,9
%A A305805 _Antti Karttunen_, Jun 13 2018