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A211191 List of odd values of k for which k^2+4 has a factor that is a square number larger than 1.

%I A211191 #36 Oct 28 2024 18:54:12
%S A211191 11,29,39,61,89,111,139,161,189,199,211,213,239,261,289,309,311,339,
%T A211191 361,365,367,389,393,411,439,461,489,511,521,539,561,589,611,639,647,
%U A211191 661,689,705,711,739,759,761,789,791,811,839,861,889,911,923,925,939,943,961,985,989
%N A211191 List of odd values of k for which k^2+4 has a factor that is a square number larger than 1.
%C A211191 Or, (odd integers n such that) n^2 + 4 is not squarefree. - _Zak Seidov_, Feb 03 2013
%H A211191 Ruskin Harding, <a href="/A211191/b211191.txt">Table of n, a(n) for n = 1..5258</a>
%e A211191 The first odd value of k for which k^2+4 has a square factor is 11: 11^2+4 = 125 = 5^2*5.
%t A211191 Select[Range[11, 1000, 2], ! SquareFreeQ[#^2 + 4] &] (* _Zak Seidov_, Feb 03 2013 *)
%o A211191 (Python)
%o A211191 b=1
%o A211191 x=1
%o A211191 for i in range(1, 100000, 2):
%o A211191     for j in range(2, i):
%o A211191        if ((i**2)+4)%(j**2)==0:
%o A211191           a=i
%o A211191           if a!=b:
%o A211191              b=a
%o A211191              print(x, i)
%o A211191              x=x+1
%o A211191 (PARI)
%o A211191 is_term(n) = !issquarefree(n^2+4);
%o A211191 forstep (n=1,10^3,2, if (is_term(n), print1(n,", ")));
%o A211191 /* _Joerg Arndt_, Feb 05 2013 */
%o A211191 (Magma) [k: k in [1..1000 by 2] | not IsSquarefree(k^2+4)]; // _Bruno Berselli_, Feb 06 2013
%Y A211191 Cf. A000290, A005117, A005408, A087475.
%K A211191 nonn
%O A211191 1,1
%A A211191 _Ruskin Harding_, Feb 03 2013