A181962 Numbers not of the form pi(p) + pi(sqrt(p)) for some prime p.

3, 6, 12, 19, 35, 45, 68, 80, 108, 156, 173, 231, 276, 297, 344, 425, 504, 537, 628, 695, 726, 833, 909, 1024, 1188, 1278, 1321, 1409, 1452, 1553, 1908, 2008, 2174, 2224, 2524, 2583, 2766, 2953, 3082, 3281, 3477, 3554, 3911, 3989, 4134, 4210, 4674, 5154, 5323

Offset: 1

Author

Vladimir Shevelev, Apr 06 2012

Keywords

• nonn

Comments

Or places of squares in A000430.

Examples

			12 is in the sequence, since pi(23)+pi(sqrt(23))=9+2=11, while pi(29)+pi(sqrt(29))=10+3=13.
Also 12 is in the sequence since A000430(12)=25 is not prime.
		

Crossrefs

Cf. A000430, A000040, A000720, A000879.

Programs

Maple

a:= n-> numtheory[pi](ithprime(n)^2)+n:
seq(a(n), n=1..50);  # Alois P. Heinz, Feb 21 2025

Mathematica

t = Table[PrimePi[n] + PrimePi[Sqrt[n]], {n, Prime[Range[10000]]}]; Complement[Range[t[[-1]]], t] (* T. D. Noe, Apr 09 2012 *)

Python

from sympy import primepi, prime
def A181962(n): return primepi(prime(n)**2)+n # Chai Wah Wu, Feb 18 2025

Formula

a(n) = pi(prime(n)^2) + n = A000879(n) + n. - Chai Wah Wu, Feb 18 2025