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%I #9 Mar 30 2012 18:35:54
%S 2,34,4,46,6,50,76,194,100,144,366,10,730,324,374,254,286,266,886,274,
%T 14,794,610,546,16,456,494,334,724,964,520,526,834,664,1596,504,3510,
%U 20,2720,1234,1120,516,566,874,810,756,1134,2110,1224,24,670,726
%N a(n) = the smallest number k such that the smallest prime factor of k^2 + 1 equals A002144(n).
%C The sequence giving the smallest number k such that the greatest prime factor of k^2 + 1 equals A002144(n) is A002314.
%e a(1) = 2 because 2^2 + 1 = 5 = A002144(1) ;
%e a(2) = 34 because 34^2 + 1= 13*89 = A002144(2) * 89 ;
%e a(3) = 4 because 4^2 + 1 = 17 = A002144(3) ;
%e a(4) = 46 because 46^2 + 1 = 29*73 = A002144(4) * 73.
%p with(numtheory):T:=array(1..200):k:=1:for p from 1 to 1000 do: if type(p,prime)=true
%p and irem(p,4)=1 then T[k]:=p:k:=k+1:else fi:od:for q from 1 to k do:z:=T[q]:ind:=0:for n from 1 to 10000 while(ind=0) do: x:=n^2+1:y:=factorset(x):if z=y[1] then ind:=1:printf(`%d, `,n):else fi:od: od:
%Y Cf. A002522, A002144, and A002314.
%K nonn
%O 1,1
%A _Michel Lagneau_, Jan 18 2011
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