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%I #11 Apr 20 2023 17:46:39
%S 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 -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 -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 Dirichlet inverse of A348717.
%H Antti Karttunen, <a href="/A354186/b354186.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A354186/a354186.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A348717(n/d) * a(d).
%F a(n) = A354187(n) - A348717(n).
%o (PARI)
%o 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 memoA354186 = Map();
%o 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 Cf. A348717, A354187.
%K sign
%O 1,2
%A _Antti Karttunen_, May 19 2022
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