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%I #7 Jul 31 2020 16:43:14
%S 0,0,2,0,1,2,2,0,1,3,2,4,3,4,4,0,3,2,2,3,3,4,4,2,0,3,3,4,1,5,3,0,2,4,
%T 2,2,3,2,4,3,3,3,4,5,3,5,2,6,4,2,5,4,4,4,5,4,4,3,2,4,3,3,4,0,5,6,3,1,
%U 3,6,5,2,5,4,6,3,3,4,4,5,2,1,5,6,5,4,4,4,3,4,5,4,4,6,4,4,4,3,4,5,3,2,4,5,4
%N a(n) = A331410(1+sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.
%H Antti Karttunen, <a href="/A336695/b336695.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A331410(1+A000203(n)) = A331410(A088580(n)) = A331410(A332459(n)).
%o (PARI)
%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 A336695(n) = A331410(1+sigma(n));
%Y Cf. A000203, A088580, A324294, A331410, A332459, A336691, A336692, A336693, A336694, A336696.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jul 31 2020
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