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A378749 Dirichlet inverse of A378747, where A378747(n) = A048673(n) - A001065(n).

%I A378749 #8 Dec 09 2024 15:25:50
%S A378749 1,-1,-2,-1,-3,2,-5,-4,-5,3,-6,-1,-8,3,3,-13,-9,-3,-11,-1,3,6,-14,-4,
%T A378749 -10,6,-22,-3,-15,-5,-18,-37,6,9,4,-7,-20,9,6,-4,-21,-7,-23,-1,-1,10,
%U A378749 -26,-10,-28,-2,9,-3,-29,-18,7,-4,9,15,-30,3,-33,14,1,-94,7,-8,-35,-1,10,-8,-36,4,-39,18,2,-3,7,-10,-41
%N A378749 Dirichlet inverse of A378747, where A378747(n) = A048673(n) - A001065(n).
%H A378749 Antti Karttunen, <a href="/A378749/b378749.txt">Table of n, a(n) for n = 1..20000</a>
%H A378749 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A378749 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378747(n/d) * a(d).
%o A378749 (PARI)
%o A378749 A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
%o A378749 A378747(n) = (A048673(n)-(sigma(n)-n));
%o A378749 memoA378749 = Map();
%o A378749 A378749(n) = if(1==n,1,my(v); if(mapisdefined(memoA378749,n,&v), v, v = -sumdiv(n,d,if(d<n,A378747(n/d)*A378749(d),0)); mapput(memoA378749,n,v); (v)));
%Y A378749 Cf. A001065, A048673, A378747.
%Y A378749 Cf. also A378750.
%K A378749 sign
%O A378749 1,3
%A A378749 _Antti Karttunen_, Dec 09 2024