

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
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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 wellknown application of the principle of inclusionexclusion 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 Plewe, Jun 12 2007


STATUS

approved



