A326067 a(n) = sigma(n) - sigma(A032742(n)) - n, where A032742 gives the largest proper divisor of n, and sigma is the sum of divisors of n.

-1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 3, 0, 0, 8, 0, 4, 3, 2, 0, 8, 0, 2, 0, 4, 0, 18, 0, 0, 3, 2, 5, 16, 0, 2, 3, 8, 0, 22, 0, 4, 9, 2, 0, 16, 0, 12, 3, 4, 0, 26, 5, 8, 3, 2, 0, 36, 0, 2, 9, 0, 5, 30, 0, 4, 3, 26, 0, 32, 0, 2, 18, 4, 7, 34, 0, 16, 0, 2, 0, 44, 5, 2, 3, 8, 0, 66, 7, 4, 3, 2, 5, 32, 0, 16, 9, 24, 0, 42, 0, 8, 39

Offset: 1

Author

Antti Karttunen, Jun 06 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A013661, A032742, A033879, A246655 (positions of zeros), A326065, A326066, A326068, A326069.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A326066(n) = (sigma(n) - sigma(A032742(n)));
A326067(n) = (A326066(n) - n);

Formula

a(n) = A326066(n) - n = A000203(n) - A000203(A032742(n)) - n.

a(n) = A326068(n) - A033879(n).

a(p^k) = 0 for all primes and all exponents k >= 1.

Sum_{k=1..n} a(k) ~ ((zeta(2) * (1 - c) - 1)/2) * n^2, where c is defined in the corresponding formula in A326065. . - Amiram Eldar, Dec 21 2024