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 A158819 (Number of squarefree numbers <= n) minus round(n/zeta(2)). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Race between the number of squarefree numbers and round(n/zeta(2)). First term < 0: a(172) = -1. REFERENCES 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. LINKS Daniel Forgues, Table of n, a(n) for n=1..100000 A. Granville, ABC means we can count squarefree FORMULA 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)). CROSSREFS 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. Cf. A005117 Squarefree numbers. Cf. A013929 Nonsquarefree numbers. Sequence in context: A238015 A257679 A056059 * A031279 A124778 A037831 Adjacent sequences:  A158816 A158817 A158818 * A158820 A158821 A158822 KEYWORD sign AUTHOR Daniel Forgues, Mar 27 2009 STATUS approved

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Last modified July 4 10:11 EDT 2022. Contains 355075 sequences. (Running on oeis4.)