A326068 a(n) = n - sigma(A032742(n)), where sigma is the sum of divisors of n and A032742 gives the largest proper divisor of n.

0, 1, 2, 1, 4, 2, 6, 1, 5, 4, 10, 0, 12, 6, 9, 1, 16, 5, 18, 2, 13, 10, 22, -4, 19, 12, 14, 4, 28, 6, 30, 1, 21, 16, 27, -3, 36, 18, 25, -2, 40, 10, 42, 8, 21, 22, 46, -12, 41, 19, 33, 10, 52, 14, 43, 0, 37, 28, 58, -12, 60, 30, 31, 1, 51, 18, 66, 14, 45, 22, 70, -19, 72, 36, 44, 16, 65, 22, 78, -10, 41, 40, 82, -12, 67, 42, 57, 4, 88, 12

Offset: 1

Author

Antti Karttunen, Jun 06 2019

Keywords

• sign

Links

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

Crossrefs

Cf. A000203, A013661, A032742, A033879, A326065, A326066, A326067, A326069.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A326065(n) = sigma(A032742(n));
A326068(n) = (n - A326065(n));

Formula

a(n) = n - A326065(n) = n - A000203(A032742(n)).

a(n) = A326067(n) + A033879(n).

Sum_{k=1..n} a(k) ~ ((1 - zeta(2) * c)/2) * n^2, where c = Sum_{p prime} ((p/((p-1)^2*(p+1))) * Product_{prime q <= p} ((q-1)^2*(q+1)/q^3)) = 0.307613599749... . - Amiram Eldar, Dec 21 2024