nohup.bash wrapper with unique, timestamped log

#!/bin/bash

function usage
{
        echo "usage nohup.bash command ..."
        exit 1
}

if (( $# == 0 )) ; then
        usage
fi

if [ ! -w . ] ; then
        echo "nohup.bash: the current working directory is not writable by you"
        exit 1
fi

logfile=` date +nohup.%Y%m%d.%H%M%S.$$.log `

nohup /usr/bin/time $* > $logfile &
bgpid=$!
echo background process id is $bgpid

sleep 1

chmod go+r $logfile
echo created file:
echo $logfile

if kill -0 $bgpid 2> /dev/null ; then
        echo background process $bgpid is running
else
        echo background process $bgpid is not running
fi