A335877 a(n) = A331410(n) - A329697(n).

0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, -1, 1, 0, 2, 0, 0, 1, -1, 0, -1, 0, 2, 0, 0, -1, 1, 1, -2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, -1, -1, 0, 1, -1, -2, 0, -2, 2, 2, 0, 1, 0, 1, -1, 0, 1, 0, 1, -1, -2, -1, 0, 1, 0, 0, 2, -1, 0, -1, 0, 2, 1, 2, 0, -1, 0, -1, 1, 0, 1, 0, -1, 3, -1, 1, 0, 2, 1, -1, -1, -2, -2, 1, 0, 1, -2, 0, 2, 2, 2, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Jun 29 2020

Keywords

• sign

Comments

Completely additive because A329697 and A331410 are.

Links

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

Crossrefs

Cf. A329697, A331410, A334861, A335875.

Cf. A335878 (positions of zeros).

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)))); };
A335877(n) = (A331410(n)-A329697(n));
\\ Or alternatively as:
A335877(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(A331410(f[k,1]+1)-A329697(f[k,1]-1)))); };

Formula

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

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