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a(n) = A331410(sigma(n)), where A331410 is totally additive with a(2) = 0 and a(p) = 1 + a(p+1) for odd primes.
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%I #7 Aug 11 2020 10:38:35

%S 0,1,0,1,1,1,0,3,2,2,1,1,1,1,1,1,2,3,2,2,0,2,1,3,1,2,2,1,3,2,0,3,1,3,

%T 1,3,3,3,1,4,2,1,2,2,3,2,1,1,4,2,2,2,3,3,2,3,2,4,3,2,1,1,2,1,2,2,3,3,

%U 1,2,2,5,4,4,1,3,1,2,2,2,4,3,2,1,3,3,3,4,4,4,1,2,0,2,3,3,2,5,3,2,4,3,2,4,1

%N a(n) = A331410(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="/A336929/b336929.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 Additive with a(p^e) = A331410(sigma(p^e)) = A331410(1+ p + p^2 + ... + p^e).

%F a(n) = A331410(A000203(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 A336929(n) = A331410(sigma(n));

%Y Cf. A000203, A331410.

%Y Cf. also A336695, A336927, A336928.

%K nonn

%O 1,8

%A _Antti Karttunen_, Aug 11 2020