A300270 - OEIS

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

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OFFSET

1,6

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.

LINKS

Table of n, a(n) for n=1..90.

FORMULA

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

PROG

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

CROSSREFS