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A349358 Dirichlet inverse of A064216, which is A064989(2n-1), where A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

%I A349358 #8 Nov 25 2021 20:34:36
%S A349358 1,-2,-3,-1,-4,5,-11,6,-4,-1,-10,3,-9,36,1,-24,-14,25,-31,38,29,-1,
%T A349358 -12,-29,-9,10,4,-11,-34,53,-59,62,27,-5,50,-41,-71,106,19,-83,-16,
%U A349358 -125,-39,98,51,-7,-58,184,32,112,-13,-15,-30,-84,-27,-170,77,79,-44,-109,-49,162,184,-84,-10,31,-85,192,-59,-75,-86
%N A349358 Dirichlet inverse of A064216, which is A064989(2n-1), where A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p.
%H A349358 Antti Karttunen, <a href="/A349358/b349358.txt">Table of n, a(n) for n = 1..16384</a>
%H A349358 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A349358 a(1) = 1; a(n) = -Sum_{d|n, d < n} A064216(n/d) * a(d).
%F A349358 a(n) = A349359(n) - A064216(n).
%o A349358 (PARI)
%o A349358 A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A349358 A064216(n) = A064989((2*n)-1);
%o A349358 memoA349358 = Map();
%o A349358 A349358(n) = if(1==n,1,my(v); if(mapisdefined(memoA349358,n,&v), v, v = -sumdiv(n,d,if(d<n,A064216(n/d)*A349358(d),0)); mapput(memoA349358,n,v); (v)));
%Y A349358 Cf. A064216, A064989, A349359, A349398.
%Y A349358 Cf. also A323893, A349125.
%K A349358 sign
%O A349358 1,2
%A A349358 _Antti Karttunen_, Nov 17 2021