In clustering, sequence number such as customer ID and dates such as purchase date should be dropped?
I think you should drop the customer ID since it's a unique identifier and won't give you any additional value.
Instead, I would be rather cautious with the date. The date can be split into year, month and day. Depending on the analysis you are doing, it might be interesting to have K-means running also with those features.
For instance, suppose that you want to check whether you have some blobs of data in a specific period of the year, you should use the month feature.