A085397 Numbers that are not perfect powers and whose squarefree part is not congruent to 1 (mod 4).

2, 3, 6, 7, 10, 11, 12, 14, 15, 18, 19, 22, 23, 24, 26, 28, 30, 31, 34, 35, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 54, 55, 56, 58, 59, 60, 62, 63, 66, 67, 70, 71, 72, 74, 75, 76, 78, 79, 82, 83, 86, 87, 88, 90, 91, 92, 94, 95, 96, 98, 99, 102, 103, 104, 106, 107, 108

Offset: 1

Author

Eric W. Weisstein, Jun 27 2003

Keywords

• nonn
• easy

Comments

Contains A016825. - Robert Israel, Mar 20 2016

The asymptotic density of this sequence is 2/3. - Amiram Eldar, Mar 09 2021

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Artin's Constant.

Crossrefs

Subsequence of A007916.

Cf. A016825.

Programs

Maple

f:= proc(n) local F,x;
  F:= ifactors(n)[2];
  if igcd(seq(f[2],f=F)) > 1 then return false fi;
  x:= mul(f[1], f = select(t -> t[2]::odd, F));
  x mod 4 <> 1;
end proc:
select(f, [$1..200]); # Robert Israel, Mar 20 2016

Mathematica

fi[n_] := fi[n] = FactorInteger[n]; perfectPowerQ[n_] := Length[uf = Union[ fi[n][[All, 2]]]] == 1 && uf[[1]] >= 2; SquareFreePart[n_] := Times @@ Apply[Power, ({#[[1]], Mod[#[[2]], 2]} & ) /@ fi[n], {1}]; ok[n_] := ! perfectPowerQ[n] && Mod[ SquareFreePart[n], 4] != 1; Select[ Range[110], ok] (* Jean-François Alcover, Jan 20 2012 *)

PARI

isok(n) = !ispower(n) && ((core(n) % 4) != 1); \\ Michel Marcus, Mar 19 2016