A079715 - OEIS

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A079715

a(n) = Pi(n)-Pi(sqrt(n)) + 1

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; text; internal format)

	OFFSET	`1,2`
	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, Mar 17 2005`
	LINKS	`Table of n, a(n) for n=1..82.`
	FORMULA	`a(n) = pi(n) - pi(sqrt(n)) + 1 = A000720(n) - A056811(n) + 1 = A056812(n) + 1.`
	CROSSREFS	`Cf. A000720, A056811.` `Sequence in context: A086389 A128622 A026256 * A030397 A205780 A204905` `Adjacent sequences: A079712 A079713 A079714 * A079716 A079717 A079718`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre, Feb 16 2003`
	EXTENSIONS	`Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, Jun 12 2007`
	STATUS	`approved`

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Last modified May 18 20:52 EDT 2013. Contains 225428 sequences.