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%I #11 Sep 08 2022 08:46:10
%S 6,80,154,290,364,376,524,586,660,734,894,1030,1104,1116,1190,1326,
%T 1400,1486,1634,1770,1856,1930,2004,2066,2226,2300,2510,2584,2596,
%U 2744,2806,2880,2966,3040,3114,3176,3250,3324,3484,3546,3620,3694,3706,3780,3854,3916
%N Numbers n such that the smallest prime divisor of n^2+1 is 37.
%C Or numbers n such that the smallest prime divisor of n^2+1 is A002313(6).
%C a(n)== 6 or 68 (mod 74).
%H Amiram Eldar, <a href="/A248530/b248530.txt">Table of n, a(n) for n = 1..10000</a>
%e 80 is in the sequence because 80^2+1= 37*173.
%t lst={};Do[If[FactorInteger[n^2+1][[1, 1]]==37, AppendTo[lst, n]], {n, 2, 4000}]; lst
%t p = 37; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[4000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* _Amiram Eldar_, Aug 16 2019 *)
%o (Magma) [n: n in [2..4000] | PrimeDivisors(n^2+1)[1] eq 37]; // _Bruno Berselli_, Oct 08 2014
%Y Cf. A089120, A002313, A209874, A248527, A248528, A248529.
%K nonn,easy
%O 1,1
%A _Michel Lagneau_, Oct 08 2014
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