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

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(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

Prog

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

Crossrefs

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

Sequence in context: A326140 A082729 A326069 * A318878 A306408 A232626

Adjacent sequences: A326065 A326066 A326067 * A326069 A326070 A326071

Keyword

sign

Author

Antti Karttunen, Jun 06 2019

Status

approved