cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

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.

Original entry on oeis.org

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

Views

Author

Arkadiusz Wesolowski, Aug 19 2017

Keywords

Comments

Another version of A057948.

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)
		

Crossrefs

Programs

  • 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;
  • 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 *)
Showing 1-1 of 1 results.