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
FORMULA
a(n) = n^2 - Sum_{k=1..n} Sum_{i=n+1..2n} sign(i mod k). - Wesley Ivan Hurt, Feb 08 2022
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 18 2002
STATUS
approved