A334861 - OEIS

%I #12 May 15 2020 04:34:39

%S 0,0,2,0,3,2,3,0,4,3,4,2,4,3,5,0,4,4,6,3,5,4,5,2,6,4,6,3,7,5,4,0,6,4,

%T 6,4,7,6,6,3,5,5,7,4,7,5,6,2,6,6,6,4,7,6,7,3,8,7,8,5,5,4,7,0,7,6,8,4,

%U 7,6,7,4,8,7,8,6,7,6,7,3,8,5,6,5,7,7,9,4,8,7,7,5,6,6,9,2,5,6,8,6,8,6,6,4,8

%N a(n) = A329697(n) + A331410(n).

%C Completely additive because A329697 and A331410 are. No 1's occur as terms.

%H Antti Karttunen, <a href="/A334861/b334861.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A329697(n) + A331410(n).

%F a(2) = 0, a(p) = 2+A329697(p-1)+A331410(p+1) for odd primes p, a(m*n) = a(m)+a(n), if m,n > 1.

%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 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 A334861(n) = (A329697(n)+A331410(n));

%o \\ Or alternatively as:

%o A334861(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(2+A329697(f[k,1]-1)+A331410(f[k,1]+1)))); };

%Y Cf. A000079 (positions of zeros), A329697, A331410, A334862.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 14 2020