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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000290, A005117, A005408, A087475.

Sequence in context: A092194 A134307 A279775 * A353043 A350420 A240678

Adjacent sequences: A211188 A211189 A211190 * A211192 A211193 A211194

Keyword

nonn

Author

Ruskin Harding, Feb 03 2013

Status

approved