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A378750 Dirichlet inverse of A377984, where A377984(n) = 2*sigma(n) - A003961(n).

%I A378750 #6 Dec 09 2024 22:04:26
%S A378750 1,-3,-3,4,-5,9,-5,0,8,15,-11,-8,-11,15,17,8,-17,-24,-17,-16,21,33,
%T A378750 -19,0,12,33,24,-8,-29,-51,-27,24,35,51,31,56,-35,51,39,0,-41,-63,-41,
%U A378750 -40,-28,57,-43,0,32,-36,53,-32,-49,-72,57,0,57,87,-59,48,-57,81,-4,88,61,-105,-65,-64,67,-93,-71,0,-69,105
%N A378750 Dirichlet inverse of A377984, where A377984(n) = 2*sigma(n) - A003961(n).
%H A378750 Antti Karttunen, <a href="/A378750/b378750.txt">Table of n, a(n) for n = 1..20000</a>
%H A378750 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>
%H A378750 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378750 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A377984(n/d) * a(d).
%o A378750 (PARI)
%o A378750 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378750 A377984(n) = (2*sigma(n) - A003961(n));
%o A378750 memoA378750 = Map();
%o A378750 A378750(n) = if(1==n,1,my(v); if(mapisdefined(memoA378750,n,&v), v, v = -sumdiv(n,d,if(d<n,A377984(n/d)*A378750(d),0)); mapput(memoA378750,n,v); (v)));
%Y A378750 Cf. A000203, A003961, A377984.
%Y A378750 Cf. also A378749.
%K A378750 sign
%O A378750 1,2
%A A378750 _Antti Karttunen_, Dec 09 2024