Tom thinks that he has devised a plan to save $1,000,000.

Every day (days 1, 2, 3, ...) he will put away $1,

every two days (days 2, 4, 6, ...) he will put away an additional $2,

every three days (days 3, 6, 9, ...) he will put away an additional $3,

every four days (days 4, 8, 12, ...) he will put away an additional $4,

every five days (days 5, 10, 15, ...) he will put away an additional $5,

every six days (days 6, 12, 18, ...) he will put away an additional $6, and

every seven days (days 7, 14, 21, ...) he will put away an additional $7.

For example: on the 4th day he will put away ($1 + $2 + $4) = $7, on the 6th day he will put away ($1 + $2 + $3 + $6) = $12

How many days would it take Tom to reach his $1,000,000 goal (he may go over on that day)?