A336694 - OEIS

%I #7 Jul 31 2020 16:43:06

%S 0,0,1,0,2,2,2,0,2,3,2,3,2,2,2,0,3,1,3,4,3,3,2,3,0,4,2,4,3,3,3,0,4,3,

%T 4,3,3,3,4,4,4,2,3,2,4,3,4,3,3,4,3,4,3,4,3,4,4,4,3,4,4,2,4,0,2,4,4,5,

%U 2,4,3,4,3,4,3,5,2,4,4,3,3,5,2,4,4,5,4,4,4,5,3,4,5,4,4,5,4,4,4,4,3,5,4,5,2

%N a(n) = A329697(1+sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.

%H Antti Karttunen, <a href="/A336694/b336694.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) = A329697(1+A000203(n)) = A329697(A088580(n)) = A329697(A332459(n)).

%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 A336694(n) = A329697(1+sigma(n));

%Y Cf. A000203, A088580, A324294, A329697, A332459, A336691, A336692, A336693, A336695, A336696.

%K nonn

%O 1,5

%A _Antti Karttunen_, Jul 31 2020