A230774 Number of primes less than first prime above square root of n.

1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

1,5

Comments

Or repeat k (prime(k)^2 - prime(k-1)^2) times, with prime(0) set to 0 for k = 1.

This sequence is useful to compute A055399 for prime numbers.

Links

Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

Formula

Repeat 1 prime(1)^2 = 4 times; for k>1, repeat k (prime(k)^2-prime(k-1)^2) = A050216(k-1) times.

a(n) - A056811(n) = characteristic function of squares of primes.

Example

a(5) = a(6) = a(7) = a(8) = a(9) = 2 because prime(1) = 2 < sqrt(5 to 9) <= prime(2) = 3.

Mathematica

Table[1 + PrimePi[Sqrt[n-1]], {n, 100}] (* Alonso del Arte, Nov 01 2013 *)

Prog

(Python)
from math import isqrt
from sympy import primepi
def A230774(n): return primepi(isqrt(n-1))+1 # Chai Wah Wu, Nov 04 2024

Crossrefs

Cf. A050216, A056811, A055399, A230775.

Sequence in context: A348242 A105517 A069624 * A056813 A125269 A077430

Adjacent sequences: A230771 A230772 A230773 * A230775 A230776 A230777

Keyword

nonn,easy

Author

Jean-Christophe Hervé, Nov 01 2013

Status

approved