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A334863 a(n) = A064097(A003961(n)).

%I A334863 #10 May 19 2020 19:14:53
%S A334863 0,2,3,4,4,5,5,6,6,6,5,7,5,7,7,8,6,8,7,8,8,7,7,9,8,7,9,9,7,9,7,10,8,8,
%T A334863 9,10,7,9,8,10,8,10,9,9,10,9,8,11,10,10,9,9,9,11,9,11,10,9,8,11,9,9,
%U A334863 11,12,9,10,9,10,10,11,8,12,9,9,11,11,10,10,9,12,12,10,9,12,10,11,10,11,8,12,10,11,10,10
%N A334863 a(n) = A064097(A003961(n)).
%C A334863 Completely additive because A003961 is fully multiplicative and A064097 is fully additive.
%H A334863 Antti Karttunen, <a href="/A334863/b334863.txt">Table of n, a(n) for n = 1..65537</a>
%F A334863 a(n) = A064097(A003961(n)).
%F A334863 a(1) = 0; and for n > 1, a(prime(k)) = A064097(prime(1+k)) for k-th prime, and a(n*m) = a(n) + a(m) if m,n > 1.
%o A334863 (PARI)
%o A334863 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
%o A334863 A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));
%o A334863 A334863(n) = A064097(A003961(n));
%o A334863 \\ Or alternatively as:
%o A334863 A334863(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*A064097(prime(1+primepi(f[k, 1])))); };
%Y A334863 Cf. A003961, A064097, A334864.
%K A334863 nonn,less
%O A334863 1,2
%A A334863 _Antti Karttunen_, May 19 2020