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A335877 a(n) = A331410(n) - A329697(n). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,17

COMMENTS

Completely additive because A329697 and A331410 are.

LINKS

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

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. A329697, A331410, A334861, A335875.

Cf. A335878 (positions of zeros).

Sequence in context: A125005 A309367 A122179 * A125203 A023565 A321925

Adjacent sequences:  A335874 A335875 A335876 * A335878 A335879 A335880

KEYWORD

sign

AUTHOR

Antti Karttunen, Jun 29 2020

STATUS

approved

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Last modified May 18 05:10 EDT 2021. Contains 343994 sequences. (Running on oeis4.)