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

1,1

Comments

Another version of A057948.

Links

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

Example

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)

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

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 *)

Prog

(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;

Crossrefs

Cf. A002144, A057948, A134441.

Sequence in context: A314679 A314680 A314681 * A057948 A314682 A379040

Adjacent sequences: A291177 A291178 A291179 * A291181 A291182 A291183

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 19 2017

Status

approved