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A158819
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(Number of squarefree numbers <= n) minus round(n/zeta(2)).
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3
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0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1
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OFFSET
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1,7
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COMMENTS
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Race between the number of squarefree numbers and round(n/zeta(2)).
First term < 0: a(172) = -1.
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REFERENCES
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G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Q. J. Math., 48 (1917), pp. 76-92.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fifth edition (1979), Clarendon Press, pp. 269-270.
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LINKS
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FORMULA
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Since zeta(2) = Sum_{i>=1} 1/(i^2) = (Pi^2)/6, we get:
a(n) = A013928(n+1) - n/Sum_{i>=1} 1/(i^2) = O(sqrt(n));
a(n) = A013928(n+1) - 6*n/(Pi^2) = O(sqrt(n)).
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CROSSREFS
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Cf. A008966 1 if n is squarefree, else 0.
Cf. A013928 Number of squarefree numbers < n.
Cf. A100112 If n is the k-th squarefree number then k else 0.
Cf. A057627 Number of nonsquarefree numbers not exceeding n.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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