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%I #6 Jun 30 2020 00:16:26
%S 0,0,0,0,1,0,-1,0,0,1,0,0,0,-1,1,0,2,0,0,1,-1,0,-1,0,2,0,0,-1,1,1,-2,
%T 0,0,2,0,0,1,0,0,1,1,-1,-1,0,1,-1,-2,0,-2,2,2,0,1,0,1,-1,0,1,0,1,-1,
%U -2,-1,0,1,0,0,2,-1,0,-1,0,2,1,2,0,-1,0,-1,1,0,1,0,-1,3,-1,1,0,2,1,-1,-1,-2,-2,1,0,1,-2,0,2,2,2,0,0,0
%N a(n) = A331410(n) - A329697(n).
%C Completely additive because A329697 and A331410 are.
%H Antti Karttunen, <a href="/A335877/b335877.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A331410(n) - A329697(n).
%F a(2) = 0, a(p) = A331410(p+1)-A329697(p-1) for odd primes p, a(m*n) = a(m)+a(n), if m,n > 1.
%o (PARI)
%o A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
%o A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
%o A335877(n) = (A331410(n)-A329697(n));
%o \\ Or alternatively as:
%o A335877(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(A331410(f[k,1]+1)-A329697(f[k,1]-1)))); };
%Y Cf. A329697, A331410, A334861, A335875.
%Y Cf. A335878 (positions of zeros).
%K sign
%O 1,17
%A _Antti Karttunen_, Jun 29 2020
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