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A216032 Numbers k such that every prime factor of k^2 + 1 is congruent to 5 (mod 8). 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A319827 A327905 A157502 * A076300 A049637 A284753
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 30 2012
STATUS
approved

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Last modified July 16 05:19 EDT 2024. Contains 374343 sequences. (Running on oeis4.)