SharePoint rest API HTTP401

I am trying to retrieve the lists of my web by REST API.

With this code I get HTTP 401. (the browser does not prompt for the credentials)

var requestUri = "http://sp13" + "/_api/web/lists";
        var requestHeaders = { "accept": "application/json;odata=verbose" };
        $.ajax({
            url: requestUri,
            async: true,
            contentType: "application/json;odata=verbose",
            headers: requestHeaders,
            success: function (data) {
                console.log("ok" + data);
            },
            error: function (msg) {
                console.log("ko"+msg);
            }
        });

with id I add dataType :'jsonp' this code, the browser ask me for the credential, but I get this error:

because its MIME type ('application/atom+xml') is not executable, and strict MIME type checking is enabled.