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 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 Robert Israel, Table of n, a(n) for n = 1..10000 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 Cf. A005574, A216032. Sequence in context: A328465 A280844 A277887 * A071966 A349521 A326781 Adjacent sequences: A216030 A216031 A216032 * A216034 A216035 A216036 KEYWORD nonn AUTHOR Michel Lagneau, Aug 30 2012 STATUS approved

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