A053683 Number of nonprimes <= prime(n)^2.

2, 5, 16, 34, 91, 130, 228, 289, 430, 695, 799, 1150, 1418, 1566, 1880, 2400, 2994, 3202, 3880, 4366, 4624, 5430, 6003, 6921, 8246, 8949, 9315, 10068, 10458, 11246, 14252, 15185, 16628, 17131, 19712, 20254, 21920, 23654, 24846, 26688, 28605

Offset: 1

Author

Labos Elemer, Feb 16 2000

Keywords

• easy
• nonn

Examples

			Up to 25 = prime(3)^2, the 16 nonprimes are 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000879.

Programs

Mathematica

a[n_] := Prime[n]^2 - PrimePi[Prime[n]^2]; Array[a, 50] (* Amiram Eldar, Feb 16 2025 *)

PARI

a(n) = prime(n)^2 - primepi(prime(n)^2); \\ Michel Marcus, Oct 28 2013

Formula

a(n) = A000040(n)^2 - A000879(n). - Jean-Christophe Hervé, Oct 27 2013