login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216033 Numbers k such that every prime factor of k^2 + 1 is congruent to 1 (mod 8). 1
4, 16, 20, 24, 36, 40, 56, 64, 84, 100, 116, 120, 124, 140, 144, 156, 160, 176, 180, 184, 196, 204, 224, 236, 240, 256, 260, 264, 276, 280, 284, 296, 300, 324, 340, 344, 384, 396, 400, 404, 420, 436, 440, 444, 464, 480, 484, 496, 516, 536, 540, 544, 556, 576 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Robert Israel, Mar 29 2020: (Start)
All terms are divisible by 4.
Includes all terms of A005574 that are divisible by 4. (End)
LINKS
EXAMPLE
64 is in the sequence because 64^2 + 1 = 17*241 and {17, 241} == 1 (mod 8).
MAPLE
with(numtheory):for n from 1 to 1000 do:x:=factorset(n^2+1):n1:=nops(x):s1:=0:for m from 1 to n1 do: if irem(x[m], 8)=1 then s1:=s1+1:else fi:od:if s1=n1 then printf(`%d, `, n):else fi:od:
# Alternative:
select(n -> numtheory:-factorset(n^2+1) mod 8 = {1}, 4*[$1..1000]); # Robert Israel, Mar 29 2020
MATHEMATICA
Select[Range[576], Union[Mod[Transpose[FactorInteger[#^2 + 1]][[1]], 8]] == {1} &] (* T. D. Noe, Aug 31 2012 *)
Select[Range[600], AllTrue[FactorInteger[#^2+1][[All, 1]], Mod[#, 8]==1&]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 31 2021 *)
PROG
(Magma) [n: n in [1..600] | forall{PrimeDivisors(n^2+1)[i]: i in [1..#PrimeDivisors(n^2+1)] | IsOne(PrimeDivisors(n^2+1)[i] mod 8)}]; // Bruno Berselli, Aug 30 2012
CROSSREFS
Sequence in context: A328465 A280844 A277887 * A071966 A349521 A326781
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 30 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)