cp's OEIS Frontend

A218563 Numbers n such that n^2 + 1 is divisible by a 4th power.

%I A218563 #15 Oct 06 2016 02:44:16
%S A218563 182,239,443,807,1068,1432,1693,2057,2318,2682,2943,3307,3568,3932,
%T A218563 4193,4557,4818,5182,5443,5807,6068,6432,6693,7057,7318,7682,7943,
%U A218563 8307,8568,8932,9193,9557,9818,10182,10443,10807,11068,11432,11693,12057,12318,12682
%N A218563 Numbers n such that n^2 + 1 is divisible by a 4th power.
%C A218563 Includes all n == 182 or 443 (mod 625). In particular, the sequence has positive asymptotic density. # _Robert Israel_, Oct 06 2016
%H A218563 Robert Israel, <a href="/A218563/b218563.txt">Table of n, a(n) for n = 1..10000</a>
%e A218563 239 is in the sequence because 239^2+1 = 57122 = 2*13^4;
%e A218563 27493 is in the sequence because 27493^2+1 = 755865050 = 2*5^2*17^4*181.
%p A218563 N:= 100000: # to get all terms <= N
%p A218563 res:= {}:
%p A218563 p:= 2;
%p A218563 while p^4 <= N^2+1 do
%p A218563   for v in map(t -> subs(t,n), [msolve(n^2+1, p^4)]) do
%p A218563     res:= res union {seq(k*p^4+v, k = 0 .. (N-v)/p^4)}
%p A218563   od;
%p A218563   p:= nextprime(p);
%p A218563 od:
%p A218563 sort(convert(res,list)); # _Robert Israel_, Oct 06 2016
%t A218563 Select[Range[2,13000],Max[Transpose[FactorInteger[#^2+1]][[2]]]>3&]
%Y A218563 Cf. A002522, A049532, A034939, A218562.
%K A218563 nonn
%O A218563 1,1
%A A218563 _Michel Lagneau_, Nov 02 2012