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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A002522, A049532, A034939, A218562.

Sequence in context: A054572 A054985 A124185 * A145297 A056091 A272361

Adjacent sequences: A218560 A218561 A218562 * A218564 A218565 A218566

Keyword

nonn

Author

Michel Lagneau, Nov 02 2012

Status

approved