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A079715 a(n) = Pi(n) - Pi(sqrt(n)) + 1. 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

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = pi(n) - pi(sqrt(n)) + 1 = A000720(n) - A056811(n) + 1 = A056812(n) + 1.

MATHEMATICA

Table[PrimePi[n] - PrimePi[Sqrt[n]] + 1, {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)

PROG

(PARI) for(n=1, 100, print1(primepi(n) - primepi(sqrt(n)) + 1, ", ")) \\ G. C. Greubel, May 13 2017

CROSSREFS

Cf. A000720, A056811, A056812.

Sequence in context: A086389 A128622 A026256 * A030397 A257213 A205780

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 S. Plewe, Jun 12 2007

STATUS

approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)