A300270 a(n) = Sum_{1 <= i <= j <= n} mu(i*j)*floor((n/i)/j).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 20, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 32, 32, 33, 34, 34, 35, 35, 35, 36, 37, 37, 37, 38, 38, 39, 40, 41, 42, 42, 42, 43, 43, 44, 44, 44, 45, 46, 47, 48, 48, 48

Offset: 1

Author

Benoit Cloitre, Mar 01 2018

Keywords

• nonn

Comments

We have Sum_{k=1..n} mu(k)*floor(n/k) = 1 and lim_{n -> infinity} Sum_{1 <= i <= j <= n} (mu(i*j)/i)/j = 1/2.

Crossrefs

Cf. A174863, A008683.

Programs

PARI

a(n) = sum(j=1, n, sum(i=1, j, moebius(i*j)*floor(n/i/j)))

Formula

a(n) ~ n/2 (n->infinity).

a(n) = (A174863(n) + n)/2. - Ridouane Oudra, May 16 2025