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A368705
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Number of squarefree numbers that are less than n, not dividing n, and relatively prime to n.
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1
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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
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} mu(k)^2 * floor(1/gcd(n,k)) * (ceiling(n/k) - floor(n/k)).
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EXAMPLE
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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.
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MATHEMATICA
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Table[Sum[MoebiusMu[k]^2*Floor[1/GCD[n, k]] (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 80}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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