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A079715
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a(n) = Pi(n)-Pi(sqrt(n)) + 1
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0
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1, 2, 3, 2, 3, 3, 4, 4, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=sum( d' dividing n, mu(d')*floor(n/d')) where each prime factor of d' is <=sqrt(n).
A well-known application of the principle of inclusion-exclusion used in sieve methods.
Number of numbers less than or equal to n and coprime to the product of the primes less than sqrt(n), i.e. to A104588(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 17 2005
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FORMULA
| a(n) = pi(n) - pi(sqrt(n)) + 1 = A000720(n) - A056811(n) + 1 = A056812(n) + 1.
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CROSSREFS
| Cf. A000720, A056811.
Sequence in context: A086389 A128622 A026256 * A030397 A205780 A204905
Adjacent sequences: A079712 A079713 A079714 * A079716 A079717 A079718
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 16 2003
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 12 2007
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