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URL: https://oeis.org/A217279

⇱ A217279 - OEIS

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A217279
Numbers of the form n^2 + 1 without prime divisors of the form a^2 + 1.
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
1,1
COMMENTS
The corresponding n are in A217276.
a(n) == 1, 17, 37, 57, 77, 97 mod 100.
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 29 2012
STATUS
approved