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

11, 29, 39, 61, 89, 111, 139, 161, 189, 199, 211, 213, 239, 261, 289, 309, 311, 339, 361, 365, 367, 389, 393, 411, 439, 461, 489, 511, 521, 539, 561, 589, 611, 639, 647, 661, 689, 705, 711, 739, 759, 761, 789, 791, 811, 839, 861, 889, 911, 923, 925, 939, 943, 961, 985, 989

Offset: 1

Author

Ruskin Harding, Feb 03 2013

Keywords

• nonn

Comments

Or, (odd integers n such that) n^2 + 4 is not squarefree. - Zak Seidov, Feb 03 2013

Examples

			The first odd value of k for which k^2+4 has a square factor is 11: 11^2+4 = 125 = 5^2*5.
		

Links

• Ruskin Harding, Table of n, a(n) for n = 1..5258

Crossrefs

Cf. A000290, A005117, A005408, A087475.

Programs

Magma

[k: k in [1..1000 by 2] | not IsSquarefree(k^2+4)]; // Bruno Berselli, Feb 06 2013

Mathematica

Select[Range[11, 1000, 2], ! SquareFreeQ[#^2 + 4] &] (* Zak Seidov, Feb 03 2013 *)

PARI

is_term(n) = !issquarefree(n^2+4);
forstep (n=1,10^3,2, if (is_term(n), print1(n,", ")));
/* Joerg Arndt, Feb 05 2013 */

Python

b=1
x=1
for i in range(1, 100000, 2):
    for j in range(2, i):
       if ((i**2)+4)%(j**2)==0:
          a=i
          if a!=b:
             b=a
             print(x, i)
             x=x+1