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

1,1

Comments

Or places of squares in A000430.

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000430, A000040, A000720, A000879.

Sequence in context: A125851 A351621 A209489 * A226220 A218076 A308722

Adjacent sequences: A181959 A181960 A181961 * A181963 A181964 A181965

Keyword

nonn,changed

Author

Vladimir Shevelev, Apr 06 2012

Status

approved