A335904 - OEIS

%I #20 Jul 09 2020 22:37:48

%S 0,0,1,0,2,1,2,0,2,2,4,1,4,2,3,0,3,2,5,2,3,4,6,1,4,4,3,2,6,3,4,0,5,3,

%T 4,2,8,5,5,2,6,3,8,4,4,6,8,1,4,4,4,4,8,3,6,2,6,6,10,3,8,4,4,0,6,5,9,3,

%U 7,4,7,2,11,8,5,5,6,5,8,2,4,6,10,3,5,8,7,4,9,4,6,6,5,8,7,1,6,4,6,4,9,4,9,4,5

%N Fully additive with a(2) = 0, and a(p) = 1+a(p-1)+a(p+1), for odd primes p.

%H Antti Karttunen, <a href="/A335904/b335904.txt">Table of n, a(n) for n = 1..65537</a>

%F Totally additive with a(2) = 0, and for odd primes p, a(p) = 1 + a(p-1) + a(p+1).

%F a(n) = A336118(n) +  A087436(n).

%F For all n >= 1, a(A335915(n)) = A336118(n).

%F For all n >= 1, a(n) >= A335884(n) >= A335881(n) >= A335875(n) >= A335885(n).

%F For all n >= 0, a(3^n) = n.

%o (PARI) A335904(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A335904(f[k,1]-1)+A335904(f[k,1]+1)))); };

%Y Cf. A000244, A052126, A087436, A171462, A335875, A335876, A335881, A335884, A335885, A335905, A335906, A335915, A336118.

%K nonn

%O 1,5

%A _Antti Karttunen_, Jun 29 2020