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A089229 Neither primes nor square numbers.

%I A089229 #32 Oct 13 2024 02:40:42
%S A089229 6,8,10,12,14,15,18,20,21,22,24,26,27,28,30,32,33,34,35,38,39,40,42,
%T A089229 44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,
%U A089229 76,77,78,80,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,102,104,105,106
%N A089229 Neither primes nor square numbers.
%C A089229 Also, composites with an even number of divisors. - _Juri-Stepan Gerasimov_, Jul 17 2009
%H A089229 Zak Seidov, <a href="/A089229/b089229.txt">Table of n, a(n) for n = 1..8671</a>
%F A089229 (1 - A010051(a(n))) * (1 - A010052(a(n))) = 1. - _Reinhard Zumkeller_, Jul 07 2014
%t A089229 m=100;Complement[Range[0,m^2],Range[0,m]^2,Prime[Range[PrimePi[m^2]]]] (* _Zak Seidov_, Dec 12 2011*)
%o A089229 (Haskell)
%o A089229 a089229 n = a089229_list !! (n-1)
%o A089229 a089229_list = f a018252_list $ tail a000290_list where
%o A089229    f (u:us) vs'@(v:vs) = if u < v then u : f us vs' else f us vs
%o A089229 -- _Reinhard Zumkeller_, Jul 07 2014
%o A089229 (PARI) lista(nn) = for (n=1, nn, if (!issquare(n) && !isprime(n), print1(n, ", "))); \\ _Michel Marcus_, Jun 01 2015
%o A089229 (PARI) is(n)=!issquare(n) && !isprime(n) \\ _Charles R Greathouse IV_, Oct 19 2015
%o A089229 (Magma) [n: n in [1..200] | not IsSquare(n) and not IsPrime(n)]; // _Vincenzo Librandi_, Jun 14 2016
%o A089229 (Python)
%o A089229 from math import isqrt
%o A089229 from sympy import primepi
%o A089229 def A089229(n):
%o A089229     def f(x): return int(n+primepi(x)+isqrt(x))
%o A089229     m, k = n, f(n)
%o A089229     while m != k: m, k = k, f(k)
%o A089229     return m # _Chai Wah Wu_, Oct 12 2024
%Y A089229 Complement of A089237.
%Y A089229 Cf. A010051, A010052, A018252, A000290.
%K A089229 nonn
%O A089229 1,1
%A A089229 _Roger L. Bagula_, Dec 10 2003