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A160764
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a(n) = n-th squarefree number minus round(n*zeta(2)).
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3
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-1, -1, -2, -2, -2, -3, -2, -2, -2, -2, -3, -3, -2, -2, -3, -3, -2, -1, -1, -2, -2, -2, -3, -2, -3, -4, -3, -4, -5, -3, -4, -2, -1, -1, -1, -1, -2, -2, -2, -1, -1, -2, -2, -2, -3, -3, -3, -2, -3, -3, -2, -3, -2, -3, -3, -3, -3, -2, -3, -4, -3, -1, -2, -2, -2, -3, -3, -3, -4
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OFFSET
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1,3
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COMMENTS
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Race between the n-th squarefree number and round(n*zeta(2)).
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..60794
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FORMULA
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Since zeta(2) = Sum[{i, 1, inf}, {1/(i^2)}] = (pi^2)/6, we get:
a(n) = A005117(n) - n * Sum[{i, 1, inf}, {1/(i^2)}] = O(sqrt(n))
a(n) = A005117(n) - n * (pi^2)/6 = O(sqrt(n))
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CROSSREFS
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Cf. A005117 Squarefree numbers.
Cf. A013929 Not squarefree numbers.
Cf. A013928 Number of squarefree numbers < n.
Cf. A158819 Number of squarefree numbers <= n minus round(n/zeta(2)).
Sequence in context: A130192 A175064 A104564 * A156384 A064656 A056608
Adjacent sequences: A160761 A160762 A160763 * A160765 A160766 A160767
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KEYWORD
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sign
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AUTHOR
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Daniel Forgues, May 26 2009
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STATUS
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approved
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