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Numbers k such that k^2 + 1 is a composite squarefree number.
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%I #16 Feb 22 2021 03:41:41

%S 3,5,8,9,11,12,13,15,17,19,21,22,23,25,27,28,29,30,31,33,34,35,37,39,

%T 42,44,45,46,47,48,49,50,51,52,53,55,58,59,60,61,62,63,64,65,67,69,71,

%U 72,73,75,76,77,78,79,80,81,83,85,86,87,88,89,91,92,95,96,97,98,100,101

%N Numbers k such that k^2 + 1 is a composite squarefree number.

%H Amiram Eldar, <a href="/A134427/b134427.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=3, because 3^2 + 1 = 10 is composite squarefree.

%e a(2)=5, because 5^2 + 1 = 26 is composite squarefree.

%e a(3)=8, because 8^2 + 1 = 50 is composite squarefree.

%p ts_fn4:=proc(n) local i,tren,ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false and numtheory[mobius] (tren) <> 0 ) then ans:=[ op(ans), i ]: fi od: RETURN(ans) end: ts_fn4(200);

%t Select[Range[100], CompositeQ[#^2+1] && SquareFreeQ[#^2+1] &] (* _Amiram Eldar_, Feb 22 2021 *)

%Y Cf. A002496, A124809, A134420.

%K nonn

%O 1,1

%A _Jani Melik_, Jan 18 2008

%E Definition corrected by _T. D. Noe_, Sep 16 2008