Javascript Sieve of Eratosthenes

Sieve of Eratosthenes

var Eratosthenes = function (n) {
    this.array = function () {
        var arr = [];
        var output = [];

        for (var i = 0; i < n; i++) {
            arr.push(i);
        }
        return arr;
    };

    this.sieve = function () {
        var sieve = this.array();
        var limit = Math.sqrt(n);
        for (var i = 2; i <= limit; i++) {
            if (sieve[i]) {
                for (var j = i * i; j < n; j += i) {
                    sieve[j] = false;
                }
            }
        }
        var arr = [];
        for (var k = 2; k < sieve.length; k++) {
            if (sieve[k]) {
                arr.push(sieve[k]);
            }
        }
        return arr;
    };
};


$("input").keypress(function (e) {
    if (e.which == 13) {
        var input = $("#input").val();

        var era = new Eratosthenes(input);
        var sieve = era.sieve().join(" ");

        $("#output").html(sieve);
    }
});

Can you please explain the time complexity as well.