A033270 - OEIS

A033270

Number of odd primes <= n.

0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 17, 17, 17, 17

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000720(n) - 1, n > 1. - Reinhard Zumkeller, Sep 15 2011

G.f.: (1/(1 - x)) * Sum_{k>=2} x^prime(k). - Ilya Gutkovskiy, Sep 14 2019

MATHEMATICA

a[1] = 0; a[n_] := PrimePi[n] - 1; Array[a, 64] (* Jean-François Alcover, Nov 28 2017 *)

PROG

(Haskell)

a033270 n = a033270_list !! (n-1)

a033270_list = 0 : 0 : scanl1 (+) (drop 2 a010051_list)

-- Reinhard Zumkeller, Sep 15 2011

(PARI) a(n)=max(primepi(n)-1, 0) \\ Charles R Greathouse IV, Jun 25 2013

(Magma) A033270:=func<n|n le 1 select 0 else #PrimesUpTo(n)-1>; // Jason Kimberley, May 15 2018

CROSSREFS

Cf. A000720, A065091, A304484.

Sequence in context: A048688 A092695 A281687 * A377899 A285507 A103264

Adjacent sequences: A033267 A033268 A033269 * A033271 A033272 A033273

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved