cp's OEIS Frontend

A354186 Dirichlet inverse of A348717.

%I A354186 #11 Apr 20 2023 17:46:39
%S A354186 1,-2,-2,0,-2,2,-2,0,0,-2,-2,4,-2,-6,2,0,-2,-2,-2,12,-2,-14,-2,0,0,
%T A354186 -18,0,20,-2,10,-2,0,-6,-26,2,8,-2,-30,-14,0,-2,30,-2,36,4,-38,-2,0,0,
%U A354186 -18,-18,44,-2,-6,-2,0,-26,-50,-2,-4,-2,-54,12,0,-6,54,-2,60,-30,2,-2,-8,-2,-66,-2,68,2,90,-2,0,0,-74
%N A354186 Dirichlet inverse of A348717.
%H A354186 Antti Karttunen, <a href="/A354186/b354186.txt">Table of n, a(n) for n = 1..10000</a>
%H A354186 Antti Karttunen, <a href="/A354186/a354186.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A354186 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A354186 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A348717(n/d) * a(d).
%F A354186 a(n) = A354187(n) - A348717(n).
%o A354186 (PARI)
%o A354186 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A354186 memoA354186 = Map();
%o A354186 A354186(n) = if(1==n,1,my(v); if(mapisdefined(memoA354186,n,&v), v, v = -sumdiv(n,d,if(d<n,A348717(n/d)*A354186(d),0)); mapput(memoA354186,n,v); (v)));
%Y A354186 Cf. A348717, A354187.
%K A354186 sign
%O A354186 1,2
%A A354186 _Antti Karttunen_, May 19 2022