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A097823 Numbers n such that n^2+n+41 (Euler's "prime generating polynomial") is not squarefree. 10


%S 40,603,798,890,917,1245,1253,1318,1640,1651,1721,2010,2069,2251,2452,

%T 2606,2649,3094,3099,3321,3402,3527,3607,4123,4239,4301,4819,4943,

%U 5002,5083,5308,5372,5425,5736,5790,5930,5958,5998,6150,6416,6511,6683,6764

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

%H Harvey P. Dale, <a href="/A097823/b097823.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>

%e 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.

%t Select[Range[10000],!SquareFreeQ[#^2+#+41]&] (* _Harvey P. Dale_, Nov 06 2011 *)

%Y 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.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Aug 26 2004

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Last modified July 26 09:58 EDT 2021. Contains 346294 sequences. (Running on oeis4.)