A085397 - OEIS (original) (raw)

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

COMMENTS

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

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:

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