A291180 Numbers of the form 4*k + 1 with k >= 1 that are not divisible by any prime factor of the form 4*m + 1, except themselves.
5, 9, 13, 17, 21, 29, 33, 37, 41, 49, 53, 57, 61, 69, 73, 77, 81, 89, 93, 97, 101, 109, 113, 121, 129, 133, 137, 141, 149, 157, 161, 173, 177, 181, 189, 193, 197, 201, 209, 213, 217, 229, 233, 237, 241, 249, 253, 257, 269, 277, 281, 293, 297, 301, 309, 313, 317
Offset: 1
Keywords
Examples
From _Michael De Vlieger_, Aug 19 2017: (Start) 5 is in the sequence because it is prime. 9 is in the sequence because the only distinct prime divisor 3 is 3 (mod 4). 25 and 45 are not in the sequence because they are divisible by 5 = 1 (mod 4). (End)
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Magma
lst:=[]; for n in [5..317 by 4] do if IsPrime(n) then Append(~lst, n); else f:=Factorization(n); if IsZero([x: x in [1..#f] | f[x][1] mod 4 eq 1]) then Append(~lst, n); end if; end if; end for; lst;
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Maple
filter:= n -> isprime(n) or andmap(t -> t mod 4 <> 1, numtheory:-factorset(n)): select(filter, [seq(i,i=5..1000,4)]); # Robert Israel, Aug 21 2017
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Mathematica
Select[4 Range[80] + 1, Function[n, If[CompositeQ@ n, NoneTrue[ Select[ FactorInteger[n][[All, 1]], Mod[#, 4] == 1 &], Divisible[n, #] &], True]]] (* Michael De Vlieger, Aug 19 2017 *)
Comments