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A248531
Numbers n such that the smallest prime divisor of n^2+1 is 41.
7
50, 114, 196, 214, 296, 624, 706, 770, 870, 934, 1034, 1180, 1280, 1426, 1444, 1590, 1690, 1754, 1836, 1936, 2000, 2164, 2246, 2264, 2346, 2574, 2674, 2756, 2820, 2984, 3066, 3084, 3230, 3330, 3394, 3494, 3576, 3640, 3740, 3886, 3904, 4214, 4296, 4460, 4624
OFFSET
1,1
COMMENTS
Or numbers n such that the smallest prime divisor of n^2+1 is A002313(7).
a(n)== 32 or 50 (mod 82).
LINKS
EXAMPLE
50 is in the sequence because 50^2+1= 41*61.
MATHEMATICA
lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==41, AppendTo[lst, n]], {n, 2, 2000}]; lst
Select[Range[5000], FactorInteger[#^2+1][[1, 1]]==41&] (* Harvey P. Dale, Aug 15 2017 *)
p = 41; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[5000], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *)
PROG
(Magma) [n: n in [2..5000] | PrimeDivisors(n^2+1)[1] eq 41]; // Bruno Berselli, Oct 08 2014
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Oct 08 2014
STATUS
approved