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A334864 a(n) = A064097(A003961(n)) - A064097(n).

%I A334864 #8 May 19 2020 19:15:00
%S A334864 0,1,1,2,1,2,1,3,2,2,0,3,0,2,2,4,1,3,1,3,2,1,0,4,2,1,3,3,0,3,0,5,1,2,
%T A334864 2,4,0,2,1,4,1,3,1,2,3,1,-1,5,2,3,2,2,1,4,1,4,2,1,-1,4,1,1,3,6,1,2,0,
%U A334864 3,1,3,-1,5,1,1,3,3,1,2,0,5,4,2,0,4,2,2,1,3,-1,4,1,2,1,0,2,6,1,3,2,4,0,3,1,3,3
%N A334864 a(n) = A064097(A003961(n)) - A064097(n).
%C A334864 Completely additive because A064097 and A334863 are.
%H A334864 Antti Karttunen, <a href="/A334864/b334864.txt">Table of n, a(n) for n = 1..65537</a>
%F A334864 a(n) = A334863(n) - A064097(n) = A064097(A003961(n)) - A064097(n).
%F A334864 a(1) = 0; and for n > 1, a(prime(k)) = A064097(prime(1+k)) - A064097(prime(k)) for k-th prime, and a(n*m) = a(n) + a(m) if m,n > 1.
%o A334864 (PARI)
%o A334864 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
%o A334864 A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));
%o A334864 A334864(n) = (A064097(A003961(n))-A064097(n));
%o A334864 \\ Or alternatively as:
%o A334864 A334864(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*(A064097(prime(1+primepi(f[k, 1])))-A064097(f[k,1]))); };
%Y A334864 Cf. A003961, A064097, A334863.
%K A334864 sign,less
%O A334864 1,4
%A A334864 _Antti Karttunen_, May 19 2020