A343224 a(n) = sigma(n) - A003415(n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

1, 2, 3, 3, 5, 7, 7, 3, 7, 11, 11, 12, 13, 15, 16, -1, 17, 18, 19, 18, 22, 23, 23, 16, 21, 27, 13, 24, 29, 41, 31, -17, 34, 35, 36, 31, 37, 39, 40, 22, 41, 55, 43, 36, 39, 47, 47, 12, 43, 48, 52, 42, 53, 39, 56, 28, 58, 59, 59, 76, 61, 63, 53, -65, 66, 83, 67, 54, 70, 85, 71, 39, 73, 75, 69, 60, 78, 97, 79, 10, 13

Offset: 1

Author

Antti Karttunen, Apr 15 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A003415, A013661, A136141.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A343224(n) = sigma(n) - A003415(n);

Formula

a(n) = A000203(n) - A003415(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Pi^2/6 - Sum_{p prime} 1/(p*(p-1)) = A013661 - A136141 = 0.871777... . - Amiram Eldar, Dec 29 2024