A216032 Numbers k such that every prime factor of k^2 + 1 is congruent to 5 (mod 8).

2, 6, 8, 10, 12, 14, 18, 26, 28, 44, 48, 52, 54, 60, 66, 68, 70, 74, 76, 80, 82, 88, 90, 92, 94, 96, 104, 108, 110, 118, 122, 126, 130, 134, 136, 138, 142, 146, 150, 152, 162, 164, 170, 182, 188, 206, 210, 218, 220, 230, 244, 248, 250, 270, 272, 282, 292, 294

Offset

1,1

Comments

From Robert Israel, Mar 29 2020: (Start)

All terms are even.

Contains all terms of A005574 that are even but not divisible by 4. (End)

Links

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

Example

28 is in the sequence because 28^2 + 1 = 5*157 and {5,157} == 5 (mod 8).

Maple

with(numtheory):for n from 1 to 300 do:x:=factorset(n^2+1):n1:=nops(x):s1:=0:for m from 1 to n1 do: if irem(x[m], 8)=5 then s1:=s1+1:else fi:od:if s1=n1 then printf(`%d, `, n):else fi:od:

Mathematica

Select[Range[294], Union[Mod[Transpose[FactorInteger[#^2 + 1]][[1]], 8]] == {5} &] (* T. D. Noe, Aug 31 2012 *)

Prog

(Magma) [n: n in [1..300] | forall{PrimeDivisors(n^2+1)[i]: i in [1..#PrimeDivisors(n^2+1)] | PrimeDivisors(n^2+1)[i] mod 8 eq 5}]; // Bruno Berselli, Aug 30 2012

Crossrefs

Cf. A002522, A215950, A215963, A215965.

Sequence in context: A319827 A327905 A157502 * A076300 A049637 A284753

Adjacent sequences: A216029 A216030 A216031 * A216033 A216034 A216035

Keyword

nonn

Author

Michel Lagneau, Aug 30 2012

Status

approved