A334861 a(n) = A329697(n) + A331410(n).

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 14 2020

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Programs

PARI

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)))); };
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)))); };
A334861(n) = (A329697(n)+A331410(n));
\\ Or alternatively as:
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)))); };

Formula

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

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.