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A335877
a(n) = A331410(n) - A329697(n).
7
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
1,17
COMMENTS
Completely additive because A329697 and A331410 are.
LINKS
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.
PROG
(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)))); };
CROSSREFS
Cf. A335878 (positions of zeros).
Sequence in context: A309367 A347709 A122179 * A125203 A023565 A321925
KEYWORD
sign
AUTHOR
Antti Karttunen, Jun 29 2020
STATUS
approved