Solution 1:

* * * * * wget -O - http://yoursite.com/tasks.php >/dev/null 2>&1

That should work for you. Just have a wget script that loads the page.

Using -O - means that the output of the web request will be sent to STDOUT (standard output)

by adding >/dev/null we instruct standard output to be redirect to a black hole. by adding 2>&1 we instruct STDERR (errors) to also be sent to STDOUT, and thus all output will be sent to a blackhole. (so it will load the website, but never write a file anywhere)

Solution 2:

You don't need the redirection, use only

* * * * * wget -qO /dev/null http://yoursite.com/tasks.php