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A368705
Number of squarefree numbers that are less than n, not dividing n, and relatively prime to n.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 03 2024
STATUS
approved