A089229 Neither primes nor square numbers.

6, 8, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106

Offset: 1

Author

Roger L. Bagula, Dec 10 2003

Keywords

• nonn

Comments

Also, composites with an even number of divisors. - Juri-Stepan Gerasimov, Jul 17 2009

Links

• Zak Seidov, Table of n, a(n) for n = 1..8671

Crossrefs

Complement of A089237.

Cf. A010051, A010052, A018252, A000290.

Programs

Haskell

a089229 n = a089229_list !! (n-1)
a089229_list = f a018252_list $ tail a000290_list where
   f (u:us) vs'@(v:vs) = if u < v then u : f us vs' else f us vs
-- Reinhard Zumkeller, Jul 07 2014

Magma

[n: n in [1..200] | not IsSquare(n) and not IsPrime(n)]; // Vincenzo Librandi, Jun 14 2016

Mathematica

m=100;Complement[Range[0,m^2],Range[0,m]^2,Prime[Range[PrimePi[m^2]]]] (* Zak Seidov, Dec 12 2011*)

PARI

lista(nn) = for (n=1, nn, if (!issquare(n) && !isprime(n), print1(n, ", "))); \\ Michel Marcus, Jun 01 2015

PARI

is(n)=!issquare(n) && !isprime(n) \\ Charles R Greathouse IV, Oct 19 2015

Python

from math import isqrt
from sympy import primepi
def A089229(n):
    def f(x): return int(n+primepi(x)+isqrt(x))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 12 2024

Formula

(1 - A010051(a(n))) * (1 - A010052(a(n))) = 1. - Reinhard Zumkeller, Jul 07 2014