A213367 Numbers that are not squares of primes.

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,2

Comments

Numbers m such that A000005(m) <> 3.

First differs from A175084 at a(29).

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Formula

a(n) = n+m+1 if n+m>=r^2 and a(n) = n+m otherwise where m = PrimePi(sqrt(n)) and r = A151800(floor(sqrt(n))) is the least prime > sqrt(n). Equivalently, a(n) = n+A056811(n)+1 if n+A056811(n)>=A230775(n+1)^2 and a(n) = n+A056811(n) otherwise. - Chai Wah Wu, Dec 01 2025

Example

4 is not in the sequence because 4 has three divisors: 1, 2, 4.

Mathematica

Delete[Range[Last[#]], List /@ #] & [Prime[Range[5]]^2] (* Paolo Xausa, Jun 27 2026 *)

Prog

(Python)
from math import isqrt
from sympy import primepi, nextprime
def A213367(n): return n+(m:=int(primepi(k:=isqrt(n))))+(n+m>=nextprime(k)**2) # Chai Wah Wu, Dec 01 2025

Crossrefs

Complement of A001248. Column 3 of A210976.

Cf. A000005, A018252, A175084, A210994, A151800, A000720, A230775, A056811.

Sequence in context: A355547 A031975 A028729 * A386267 A175084 A171519

Adjacent sequences: A213364 A213365 A213366 * A213368 A213369 A213370

Keyword

nonn,easy,changed

Author

Omar E. Pol, Aug 11 2012

Status

approved