A291180 - OEIS

%I #23 Sep 08 2022 08:46:19

%S 5,9,13,17,21,29,33,37,41,49,53,57,61,69,73,77,81,89,93,97,101,109,

%T 113,121,129,133,137,141,149,157,161,173,177,181,189,193,197,201,209,

%U 213,217,229,233,237,241,249,253,257,269,277,281,293,297,301,309,313,317

%N 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.

%C Another version of A057948.

%H Robert Israel, <a href="/A291180/b291180.txt">Table of n, a(n) for n = 1..10000</a>

%e From _Michael De Vlieger_, Aug 19 2017: (Start)

%e 5 is in the sequence because it is prime.

%e 9 is in the sequence because the only distinct prime divisor 3 is 3 (mod 4).

%e 25 and 45 are not in the sequence because they are divisible by 5 = 1 (mod 4).

%e (End)

%p filter:= n -> isprime(n) or andmap(t -> t mod 4 <> 1, numtheory:-factorset(n)):

%p select(filter, [seq(i,i=5..1000,4)]); # _Robert Israel_, Aug 21 2017

%t 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 *)

%o (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;

%Y Cf. A002144, A057948, A134441.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 19 2017