A097823 Numbers n such that n^2+n+41 (Euler's "prime generating polynomial") is not squarefree.

40, 603, 798, 890, 917, 1245, 1253, 1318, 1640, 1651, 1721, 2010, 2069, 2251, 2452, 2606, 2649, 3094, 3099, 3321, 3402, 3527, 3607, 4123, 4239, 4301, 4819, 4943, 5002, 5083, 5308, 5372, 5425, 5736, 5790, 5930, 5958, 5998, 6150, 6416, 6511, 6683, 6764

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Example

a(1)=40: p(40)=40^2+40+41=1681=41^2, a(2)=603: p(603)=364253=197*43^2, a(11)=1721: p(1721)=2963603=43*41^3, a(68)=10428: p(10428)=108753653=743^2*197, a(91)=14144: p(14144)=200066921=47^4*41.

Mathematica

Select[Range[10000], !SquareFreeQ[#^2+#+41]&] (* Harvey P. Dale, Nov 06 2011 *)

Crossrefs

Cf. A013929 n is not squarefree, A002837 n such that n^2-n+41 is prime, A007634 n such that n^2+n+41 is composite, A005846 primes of form n^2+n+41, A097822 n^2+n+41 has more than 2 prime factors.

Sequence in context: A374241 A372977 A269497 * A263953 A002847 A057808

Adjacent sequences: A097820 A097821 A097822 * A097824 A097825 A097826

Keyword

nonn

Author

Hugo Pfoertner, Aug 26 2004

Status

approved