A134427 Numbers k such that k^2 + 1 is a composite squarefree number.
3, 5, 8, 9, 11, 12, 13, 15, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 34, 35, 37, 39, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 58, 59, 60, 61, 62, 63, 64, 65, 67, 69, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88, 89, 91, 92, 95, 96, 97, 98, 100, 101
Offset: 1
Keywords
Examples
a(1)=3, because 3^2 + 1 = 10 is composite squarefree. a(2)=5, because 5^2 + 1 = 26 is composite squarefree. a(3)=8, because 8^2 + 1 = 50 is composite squarefree.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
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);
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Mathematica
Select[Range[100], CompositeQ[#^2+1] && SquareFreeQ[#^2+1] &] (* Amiram Eldar, Feb 22 2021 *)
Extensions
Definition corrected by T. D. Noe, Sep 16 2008