|
%I #31 Sep 08 2022 08:46:02
%S 11,29,39,61,89,111,139,161,189,199,211,213,239,261,289,309,311,339,
%T 361,365,367,389,393,411,439,461,489,511,521,539,561,589,611,639,647,
%U 661,689,705,711,739,759,761,789,791,811,839,861,889,911,923,925,939,943,961,985,989
%N List of odd values of k for which k^2+4 has a factor that is a square number larger than 1.
%C Or, (odd integers n such that) n^2 + 4 is not squarefree. - _Zak Seidov_, Feb 03 2013
%H Ruskin Harding, <a href="/A211191/b211191.txt">Table of n, a(n) for n = 1..5258</a>
%e 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 Select[Range[11, 1000, 2], ! SquareFreeQ[#^2 + 4] &] (* _Zak Seidov_, Feb 03 2013 *)
%o (Python)
%o b=1
%o x=1
%o for i in range(1, 100000, 2):
%o ....for j in range(2, i):
%o .......if ((i**2)+4)%(j**2)==0:
%o ..........a=i
%o ..........if a!=b:
%o .............b=a
%o .............print(x,i)
%o .............x=x+1
%o (PARI)
%o is_term(n) = !issquarefree(n^2+4);
%o forstep (n=1,10^3,2, if (is_term(n), print1(n,", ")));
%o /* _Joerg Arndt_, Feb 05 2013 */
%o (Magma) [k: k in [1..1000 by 2] | not IsSquarefree(k^2+4)]; // _Bruno Berselli_, Feb 06 2013
%Y Cf. A000290, A005117, A005408, A087475.
%K nonn
%O 1,1
%A _Ruskin Harding_, Feb 03 2013
%E b-file calculated to more decimal places.
%E Python program improved.
|
