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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. 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 (list; graph; refs; listen; history; text; internal format)
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 * A240678 A087693 A106017

Adjacent sequences:  A211188 A211189 A211190 * A211192 A211193 A211194

KEYWORD

nonn

AUTHOR

Ruskin Harding, Feb 03 2013

EXTENSIONS

b-file calculated to more decimal places.

Python program improved.

STATUS

approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)