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A174492 a(n) = the smallest k such that k^2+1 = p*A002144(n)^2, p prime of A002144 .

%I A174492 #16 Mar 30 2012 18:35:52
%S A174492 18,70,540,800,1486,2984,500,6760,776,4060,5604,4030,5744,1710,1744,
%T A174492 46146,186174,162886,62064,32150,37416,16610,26884,15006,130026,58724
%N A174492 a(n) = the smallest k such that k^2+1 = p*A002144(n)^2, p prime of A002144 .
%C A174492 A002144 are the primes of the form 4q + 1.
%e A174492 a(1) = 18 because 18^2 + 1 = 13*A002144(1) ^2 = 13*5^2 ;
%e A174492 a(2) = 70 because 70^2 + 1 = 29*A002144(2) ^2 = 29*13^2 ;
%e A174492 a(3) = 540 because 540^2 + 1 = 1009*A002144(3) ^2 = 1009*17^2 .
%p A174492 with(numtheory):nn:=400:T:=array(1..nn):k:=1:for x from 1 to nn do: p:=4*x+1:if
%p A174492   type(p,prime)=true then T[k]:=p:k:=k+1:else fi:od:for n from 1 to k do: ind:=0:for
%p A174492   m from 1 to 500000 while(ind=0) do:y:=m^2+1:x:= factorset(y) : n1:=nops(x):n2
%p A174492   :=bigomega(y):if n1=2 and n2 = 3 and x[1]=T[n] and ind=0 then ind:=1:printf(`%d,
%p A174492   `,m):else fi:od:od:
%Y A174492 Cf. A002144 A059321.
%K A174492 nonn
%O A174492 1,1
%A A174492 _Michel Lagneau_, Jan 25 2011