A217276 Numbers n such that no prime divisors of n^2 + 1 are of the form a^2 + 1.

34, 44, 46, 50, 60, 70, 76, 86, 96, 100, 104, 114, 136, 144, 164, 186, 190, 194, 196, 214, 220, 226, 244, 246, 254, 266, 274, 286, 294, 296, 304, 316, 320, 324, 330, 334, 346, 354, 356, 360, 366, 374, 390, 410, 416, 424, 426, 434, 454, 456, 460, 476, 484, 486

Offset: 1

Author

Michel Lagneau, Sep 29 2012

Keywords

• nonn

Examples

			34 is in the sequence because 34^2+1 = 1157 = 13*89 and the prime divisors 13, 89 are not of the form a^2+1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002522, A005574, A070303, A181436, A180252, A181436.

Programs

Maple

with(numtheory):for n from 1 to 100 do: x:=factorset(n^2+1):n1:=nops(x):ii:=0:for m from 1 to n1 do:y:=sqrt(x[m]-1):if y=floor(y) then ii:=1:else fi:od:if ii=0 then printf(`%d, `,n):else fi:od:

Mathematica

fQ[n_] := Module[{lst = Transpose[FactorInteger[n^2 + 1]][[1]]}, Length[lst] > 1 && And @@ (Not /@ IntegerQ /@ Sqrt[lst - 1])]; Select[Range[500], fQ] (* T. D. Noe, Oct 01 2012 *)