A181436 Numbers k such that the prime divisors of k^2 + 1 are of the form q^2 + 1.

1, 2, 3, 4, 6, 7, 10, 13, 14, 16, 20, 24, 26, 36, 38, 40, 43, 54, 56, 66, 68, 74, 84, 90, 94, 110, 116, 117, 120, 124, 126, 130, 134, 146, 150, 156, 160, 170, 176, 180, 183, 184, 204, 206, 210, 224, 230, 236, 240, 250, 256, 260, 264, 270, 280, 284, 293, 300, 306, 314, 326, 327

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..1000

Example

183 is in the sequence because 183^2 + 1 = 2*5*17*197 and 2 = 1^2 + 1, 5 = 2^2+1, 17 = 4^2+1 and 197 = 14^2 + 1.

Maple

with(numtheory):nn:=1000:for n from 1 to nn do: x:=n^2+1:y:=factorset(x):ny:=nops(y):id:=0:for
  q from 1 to ny do: z:=y[q]-1:zz:=sqrt(z):if zz=floor(zz) then id:=id+1:else  fi:od:if id=ny then printf(`%d, `, n):else fi:od:

Mathematica

Select[Range@330, And @@ IntegerQ /@ Sqrt[FactorInteger[#^2 + 1][[All, 1]] - 1] &] (* Ivan Neretin, Aug 31 2016 *)

Prog

(PARI) isok(n) = {fn = factor(n^2+1)[, 1]; for (k=1, #fn, if (!issquare(fn[k]-1), return (0)); ); 1; } \\ Michel Marcus, Sep 01 2016

Crossrefs

Cf. A180252, A002144, A002522, A005574.

Sequence in context: A336815 A355979 A119793 * A199118 A035941 A039854

Adjacent sequences: A181433 A181434 A181435 * A181437 A181438 A181439

Keyword

nonn

Author

Michel Lagneau, Jan 29 2011

Status

approved