Estou recebendo erro quando tento baixar este arquivo na API 23. funciona bem na versão <23. Vi perguntas semelhantes como essa, mas nenhuma solução funcionou para mim. Estou recebendo exceção para acesso de leitura e gravação .. Como conceder permissão de acesso de leitura e gravação no marshmallow ..?

Dei permissão de leitura e gravação no manifesto do Android como este.

<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
    <uses-permission android:name="android.permission.READ_PHONE_STATE" />
    <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />

Download.java

import java.io.File;

import android.app.Activity;
import android.app.DownloadManager;
import android.content.BroadcastReceiver;
import android.content.Context;
import android.content.Intent;
import android.content.IntentFilter;
import android.database.Cursor;
import android.net.Uri;
import android.os.Bundle;
import android.os.Environment;
import android.util.Log;
import android.view.View;
import android.widget.Toast;


public class Download extends Activity {
  private DownloadManager mgr=null;
  private long lastDownload=-1L;

  @Override
  public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_download);

    mgr=(DownloadManager)getSystemService(DOWNLOAD_SERVICE);
    registerReceiver(onComplete,
                     new IntentFilter(DownloadManager.ACTION_DOWNLOAD_COMPLETE));
    registerReceiver(onNotificationClick,
                     new IntentFilter(DownloadManager.ACTION_NOTIFICATION_CLICKED));


  }

  @Override
  public void onDestroy() {
    super.onDestroy();

    unregisterReceiver(onComplete);
    unregisterReceiver(onNotificationClick);
  }

  public void startDownload(View v) {
    Uri uri=Uri.parse("http://oursite/pictures/image.jpg");


    Environment
      .getExternalStoragePublicDirectory(Environment.DIRECTORY_DOWNLOADS)
      .mkdirs();

    lastDownload=
      mgr.enqueue(new DownloadManager.Request(uri)
                  .setAllowedNetworkTypes(DownloadManager.Request.NETWORK_WIFI |
                                          DownloadManager.Request.NETWORK_MOBILE)
                  .setAllowedOverRoaming(false)
                  .setTitle("Pictures")
                  //.setDescription("Something useful. No, really.")
                  .setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS,
                                                     "aadhar.jpg"));

    v.setEnabled(false);
    //findViewById(R.id.query).setEnabled(true);

  }

  public void queryStatus(View v) {
    Cursor c=mgr.query(new DownloadManager.Query().setFilterById(lastDownload));

    if (c==null) {
      Toast.makeText(this, "Update not found!", Toast.LENGTH_LONG).show();
    }
    else {
      c.moveToFirst();

      Log.d(getClass().getName(), "COLUMN_ID: "+
            c.getLong(c.getColumnIndex(DownloadManager.COLUMN_ID)));
      Log.d(getClass().getName(), "COLUMN_BYTES_DOWNLOADED_SO_FAR: "+
            c.getLong(c.getColumnIndex(DownloadManager.COLUMN_BYTES_DOWNLOADED_SO_FAR)));
      Log.d(getClass().getName(), "COLUMN_LAST_MODIFIED_TIMESTAMP: "+
            c.getLong(c.getColumnIndex(DownloadManager.COLUMN_LAST_MODIFIED_TIMESTAMP)));
      Log.d(getClass().getName(), "COLUMN_LOCAL_URI: "+
            c.getString(c.getColumnIndex(DownloadManager.COLUMN_LOCAL_URI)));
      Log.d(getClass().getName(), "COLUMN_STATUS: "+
            c.getInt(c.getColumnIndex(DownloadManager.COLUMN_STATUS)));
      Log.d(getClass().getName(), "COLUMN_REASON: "+
            c.getInt(c.getColumnIndex(DownloadManager.COLUMN_REASON)));

      Toast.makeText(this, statusMessage(c), Toast.LENGTH_LONG).show();
    }
  }

  public void viewLog(View v) {
    startActivity(new Intent(DownloadManager.ACTION_VIEW_DOWNLOADS));
  }

  private String statusMessage(Cursor c) {
    String msg="???";

    switch(c.getInt(c.getColumnIndex(DownloadManager.COLUMN_STATUS))) {
      case DownloadManager.STATUS_FAILED:
        msg="Update failed!";
        break;

      case DownloadManager.STATUS_PAUSED:
        msg="Update paused!";
        break;

      case DownloadManager.STATUS_PENDING:
        msg="Update pending!";
        break;

      case DownloadManager.STATUS_RUNNING:
        msg="Update in progress!";
        break;

      case DownloadManager.STATUS_SUCCESSFUL:
        msg="Update complete!";
        break;

      default:
        msg="Update software is nowhere in sight";
        break;
    }

    return(msg);
  }

  BroadcastReceiver onComplete=new BroadcastReceiver() {
    public void onReceive(Context ctxt, Intent intent) {
      findViewById(R.id.start).setEnabled(true);
    }
  };

  BroadcastReceiver onNotificationClick=new BroadcastReceiver() {
    public void onReceive(Context ctxt, Intent intent) {
      Toast.makeText(ctxt, "Ummmm...hi!", Toast.LENGTH_LONG).show();
    }
  };
}