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%I #11 Apr 21 2022 17:23:54
%S 1,1,-1,-1,1,1,-1,2,2,-1,1,-3,-1,1,-3,-5,1,-1,-1,3,3,-1,1,10,-1,1,-5,
%T -3,-1,1,1,14,-3,-1,1,0,-1,1,3,-10,1,-1,-1,3,10,-1,1,-35,2,2,-3,-3,-1,
%U 2,-1,10,3,1,1,3,-1,-1,-10,-42,1,1,1,3,-3,-3,-1,10,1,1,0,-3,-3,-1,-1,35,14,-1,1,-3,-1,1,3,-10
%N Dirichlet inverse of A353467.
%H Antti Karttunen, <a href="/A353468/b353468.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} A353467(n/d) * a(d).
%F a(n) = A353467(A252463(n)).
%F For all n >= 1, a(A000040(n)) = ((-1)^(n-1)).
%o (PARI)
%o A252463(n) = if(!(n%2),n/2,my(f=factor(n)); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f));
%o memoA353467 = Map();
%o A353467(n) = if(1==n,1,my(v); if(mapisdefined(memoA353467,n,&v), v, v = -sumdiv(n,d,if(d<n,A353467(A252463(n/d))*A353467(d),0)); mapput(memoA353467,n,v); (v)));
%o A353468(n) = A353467(A252463(n));
%Y Cf. A000040, A252463, A353467 [Dirichlet inverse], A353469 [sum with it].
%Y Cf. also A353458.
%K sign
%O 1,8
%A _Antti Karttunen_, Apr 21 2022
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