A077024 a(n) = Sum_{k=1..n} floor(n/k + 1/2).

1, 3, 6, 8, 12, 15, 18, 22, 26, 29, 34, 37, 41, 46, 51, 53, 58, 64, 67, 72, 77, 80, 87, 90, 95, 100, 105, 110, 115, 120, 123, 129, 136, 139, 146, 150, 153, 160, 167, 170, 176, 181, 186, 191, 198, 203, 208, 213, 217, 225, 230, 233, 242, 247, 252, 257, 262, 267

Offset

1,2

Comments

Number of ways the numbers from 1..n can divide the numbers from n+1..2n. For example, a(4) = 8; there are 8 ways that the numbers from 1..4 divide the numbers 5..8. 1 divides 5,6,7,8 (4 ways) + 2 divides 6,8 (2 ways) + 3 divides 6 (1 way) + 4 divides 8 (1 way) = 8 ways. - Wesley Ivan Hurt, Feb 07 2022

Links

Table of n, a(n) for n=1..58.

Formula

a(n) = n^2 - Sum_{k=1..n} Sum_{i=n+1..2n} sign(i mod k). - Wesley Ivan Hurt, Feb 08 2022

From Ridouane Oudra, Oct 07 2025: (Start)

a(n) = A000290(n) - A351355(n).

a(n) = A056549(n) - A000027(n).

a(n) = A062550(n) - A156745(n).

a(n) = A056548(n) - A347286(n).

a(n) = A006218(n) + A075989(n).

a(n) = A006591(n) + A069283(n). (End)

Example

[4/1 + 1/2] + [4/2 + 1/2] + [4/3 + 1/2] + [4/4 + 1/2] = 4+2+1+1 = 8 = a(4).

Prog

(PARI) a(n) = sum(k=1, n, floor(n/k+1/2)); \\ Michel Marcus, Feb 07 2022

Crossrefs

Cf. A006218, A006590, A077025, A351355, A062550, A156745.

Cf. A056548, A056549, A347286, A075989, A006591, A069283, A000290.

Sequence in context: A118335 A189630 A298793 * A338722 A185549 A185597

Adjacent sequences: A077021 A077022 A077023 * A077025 A077026 A077027

Keyword

nonn

Author

Clark Kimberling, Oct 18 2002

Status

approved