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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 19 03:48 EST 2019. Contains 329310 sequences. (Running on oeis4.)