A304484 -id:A304484 - cp's OEIS frontend

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

Offset: 1

N. J. A. Sloane

nonn

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

Cf. A000720, A065091, A304484.

a033270 n = a033270_list !! (n-1)
a033270_list = 0 : 0 : scanl1 (+) (drop 2 a010051_list)
-- Reinhard Zumkeller, Sep 15 2011

A033270:=func; // Jason Kimberley, May 15 2018

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

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

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

A304483 a(n) = pi(n)*pi(2n), where pi is A000720: the prime counting function.

Original entry on oeis.org

0, 2, 6, 8, 12, 15, 24, 24, 28, 32, 40, 45, 54, 54, 60, 66, 77, 77, 96, 96, 104, 112, 126, 135, 135, 135, 144, 144, 160, 170, 198, 198, 198, 209, 209, 220, 252, 252, 252, 264, 286, 299, 322, 322, 336, 336, 360, 360, 375, 375, 390, 405, 432, 448, 464, 464, 480, 480, 510

Offset: 1

Jason Kimberley, May 13 2018

Jason Kimberley, Table of n, a(n) for n = 1..10000

Cf. A304484(n) = A033270(n)*A033270(2n).

Cf. A291440, A291538, A291539, A291540,

A000720:=func;
A304483:=funcA000720(n)*A000720(2*n)>;
[A304483(n):n in[1..59]];

Array[PrimePi[#] PrimePi[2 #] &, 59] (* Michael De Vlieger, May 27 2018 *)

a(n) = primepi(n) * primepi(2*n); \\ Michel Marcus, May 27 2018

cp's OEIS Frontend

A033270 Number of odd primes <= n.

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