The outer double quotes should be removed, and it's an error to use both & and ; to terminate a statement - see for example Using bash "&" operator with ";" delineator?
As well, cron runs jobs using /bin/sh by default which doesn't support brace expansion or the &> combined redirection - so either replace those with POSIX equivalents:
* * * * * usertorunas for i in $(seq 1 6) ; do curl -s 'https://www.example.com/path' >/dev/null 2>&1 & done
or set SHELL=/bin/bash before the job
SHELL=/bin/bash
* * * * * usertorunas for i in {1..6} ; do curl -s 'https://www.example.com/path' &>/dev/null & done