A336386 a(n) = bigomega(sigma(n)) - bigomega(n), where bigomega (A001222) gives the number of prime factors with multiplicity, and sigma (A000203) gives the sum of divisors.

0, 0, 1, -1, 1, 1, 2, -1, -1, 1, 2, 0, 1, 2, 2, -3, 2, -1, 2, 0, 3, 2, 3, 0, -1, 1, 1, 1, 2, 2, 4, -2, 3, 2, 3, -2, 1, 2, 2, 0, 2, 3, 2, 1, 0, 3, 4, -2, 0, -1, 3, 0, 3, 1, 3, 1, 3, 2, 3, 1, 1, 4, 1, -5, 2, 3, 2, 1, 4, 3, 4, -2, 1, 1, 0, 1, 4, 2, 4, -2, -2, 2, 3, 2, 3, 2, 3, 1, 3, 0, 3, 2, 5, 4, 3, -1, 2, 0, 1, -2, 2, 3, 3, 0, 4

Offset: 1

Author

Antti Karttunen, Jul 20 2020

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A001222, A058063.

Cf. A336356, A336359 (positions of negative terms), A336360 (of nonnegative terms).

Programs

PARI

A336386(n) = (bigomega(sigma(n)) - bigomega(n));

Formula

a(n) = A058063(n) - A001222(n).

Additive with a(p^e) = A001222(A000203(p^e)) - A001222(p^e) = A001222(1 + p + p^2 + ... + p^e) - e.