A217279 Numbers of the form n^2 + 1 without prime divisors of the form a^2 + 1.

1157, 1937, 2117, 2501, 3601, 4901, 5777, 7397, 9217, 10001, 10817, 12997, 18497, 20737, 26897, 34597, 36101, 37637, 38417, 45797, 48401, 51077, 59537, 60517, 64517, 70757, 75077, 81797, 86437, 87617, 92417, 99857, 102401, 104977, 108901, 111557, 119717

Offset: 1

Author

Michel Lagneau, Sep 29 2012

Keywords

• nonn

Comments

The corresponding n are in A217276.

a(n) == 1, 17, 37, 57, 77, 97 mod 100.

Examples

			1157 is in the sequence because 1157 = 34^2 + 1 = 13*89 and the numbers 13, 89 are not of the form 1 plus a square.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002522, A005574, A217276, A181436, A180252.

Programs

Maple

isA217279 := proc(n)
    if issqr(n-1) then
        for d in numtheory[factorset](n) do
            if issqr(d-1) then
                return false;
            end if;
        end do:
        return true ;
    else
        false;
    end if;
end proc:
for n from 1 to 300 do
    if isA217279(n^2+1) then
        printf("%d ",n^2+1) ;
    end if;
end do: # R. J. Mathar, Oct 01 2012

Mathematica

Select[1 + Range[400]^2, Not[PrimeQ[#]] && Intersection[Divisors[#], 1 + Range[Sqrt[# - 1] - 1]^2] == {} &] (* Alonso del Arte, Sep 29 2012 *)