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A218563
Numbers n such that n^2 + 1 is divisible by a 4th power.
4
182, 239, 443, 807, 1068, 1432, 1693, 2057, 2318, 2682, 2943, 3307, 3568, 3932, 4193, 4557, 4818, 5182, 5443, 5807, 6068, 6432, 6693, 7057, 7318, 7682, 7943, 8307, 8568, 8932, 9193, 9557, 9818, 10182, 10443, 10807, 11068, 11432, 11693, 12057, 12318, 12682
OFFSET
1,1
COMMENTS
Includes all n == 182 or 443 (mod 625). In particular, the sequence has positive asymptotic density. # Robert Israel, Oct 06 2016
LINKS
EXAMPLE
239 is in the sequence because 239^2+1 = 57122 = 2*13^4;
27493 is in the sequence because 27493^2+1 = 755865050 = 2*5^2*17^4*181.
MAPLE
N:= 100000: # to get all terms <= N
res:= {}:
p:= 2;
while p^4 <= N^2+1 do
for v in map(t -> subs(t, n), [msolve(n^2+1, p^4)]) do
res:= res union {seq(k*p^4+v, k = 0 .. (N-v)/p^4)}
od;
p:= nextprime(p);
od:
sort(convert(res, list)); # Robert Israel, Oct 06 2016
MATHEMATICA
Select[Range[2, 13000], Max[Transpose[FactorInteger[#^2+1]][[2]]]>3&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 02 2012
STATUS
approved