A368705 Number of squarefree numbers that are less than n, not dividing n, and relatively prime to n.

0, 0, 1, 1, 2, 1, 4, 3, 3, 2, 6, 3, 7, 4, 5, 6, 10, 5, 11, 6, 7, 8, 14, 7, 12, 9, 12, 8, 16, 7, 18, 12, 12, 12, 14, 10, 22, 14, 16, 13, 25, 10, 27, 16, 17, 17, 29, 14, 25, 16, 20, 18, 31, 15, 24, 19, 22, 22, 35, 14, 36, 24, 25, 25, 29, 17, 40, 25, 28, 21, 43, 21, 44

Offset

1,5

Links

Table of n, a(n) for n=1..73.

Formula

a(n) = Sum_{k=1..n} mu(k)^2 * floor(1/gcd(n,k)) * (ceiling(n/k) - floor(n/k)).

Example

a(7) = 4. There are 4 squarefree numbers that are less than 7, do not divide 7, and relatively prime to 7: namely {2, 3, 5, 6}, so a(7) = 4.

Mathematica

Table[Sum[MoebiusMu[k]^2*Floor[1/GCD[n, k]] (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 80}]

Crossrefs

Cf. A008683 (mu), A368706.

Sequence in context: A159931 A159755 A215534 * A304573 A094322 A136757

Adjacent sequences: A368702 A368703 A368704 * A368706 A368707 A368708

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 03 2024

Status

approved