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

Author

Hugo Pfoertner, Aug 26 2004

Keywords

• nonn

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

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.

Programs

Mathematica

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