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%I #14 Sep 11 2019 06:58:15
%S 34,44,46,50,60,70,76,86,96,100,104,114,136,144,164,186,190,194,196,
%T 214,220,226,244,246,254,266,274,286,294,296,304,316,320,324,330,334,
%U 346,354,356,360,366,374,390,410,416,424,426,434,454,456,460,476,484,486
%N Numbers n such that no prime divisors of n^2 + 1 are of the form a^2 + 1.
%H Amiram Eldar, <a href="/A217276/b217276.txt">Table of n, a(n) for n = 1..10000</a>
%e 34 is in the sequence because 34^2+1 = 1157 = 13*89 and the prime divisors 13, 89 are not of the form a^2+1.
%p with(numtheory):for n from 1 to 100 do: x:=factorset(n^2+1):n1:=nops(x):ii:=0:for m from 1 to n1 do:y:=sqrt(x[m]-1):if y=floor(y) then ii:=1:else fi:od:if ii=0 then printf(`%d, `,n):else fi:od:
%t fQ[n_] := Module[{lst = Transpose[FactorInteger[n^2 + 1]][[1]]}, Length[lst] > 1 && And @@ (Not /@ IntegerQ /@ Sqrt[lst - 1])]; Select[Range[500], fQ] (* _T. D. Noe_, Oct 01 2012 *)
%Y Cf. A002522, A005574, A070303, A181436, A180252, A181436.
%K nonn
%O 1,1
%A _Michel Lagneau_, Sep 29 2012
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