cp's OEIS Frontend

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

%I A217279 #15 Sep 11 2019 06:58:18
%S A217279 1157,1937,2117,2501,3601,4901,5777,7397,9217,10001,10817,12997,18497,
%T A217279 20737,26897,34597,36101,37637,38417,45797,48401,51077,59537,60517,
%U A217279 64517,70757,75077,81797,86437,87617,92417,99857,102401,104977,108901,111557,119717
%N A217279 Numbers of the form n^2 + 1 without prime divisors of the form a^2 + 1.
%C A217279 The corresponding n are in A217276.
%C A217279 a(n) == 1, 17, 37, 57, 77, 97 mod 100.
%H A217279 Amiram Eldar, <a href="/A217279/b217279.txt">Table of n, a(n) for n = 1..10000</a>
%e A217279 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.
%p A217279 isA217279 := proc(n)
%p A217279     if issqr(n-1) then
%p A217279         for d in numtheory[factorset](n) do
%p A217279             if issqr(d-1) then
%p A217279                 return false;
%p A217279             end if;
%p A217279         end do:
%p A217279         return true ;
%p A217279     else
%p A217279         false;
%p A217279     end if;
%p A217279 end proc:
%p A217279 for n from 1 to 300 do
%p A217279     if isA217279(n^2+1) then
%p A217279         printf("%d ",n^2+1) ;
%p A217279     end if;
%p A217279 end do: # _R. J. Mathar_, Oct 01 2012
%t A217279 Select[1 + Range[400]^2, Not[PrimeQ[#]] && Intersection[Divisors[#], 1 + Range[Sqrt[# - 1] - 1]^2] == {} &] (* _Alonso del Arte_, Sep 29 2012 *)
%Y A217279 Cf. A002522, A005574, A217276, A181436, A180252.
%K A217279 nonn
%O A217279 1,1
%A A217279 _Michel Lagneau_, Sep 29 2012