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

1,1

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.

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 *)

Prog

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

Crossrefs

Subsequence of A007916.

Cf. A016825.

Sequence in context: A328832 A263881 A208892 * A307414 A073439 A188084

Adjacent sequences: A085394 A085395 A085396 * A085398 A085399 A085400

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 27 2003

Status

approved