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WEEKDAYを使用する方法 WEEKOFYEAR

SELECT WEEKOFYEAR(date) AS week, date
FROM myTable
WHERE date BETWEEN start_date AND end_date
ORDER BY week

更新 この質問はソースです

SELECT  (WEEK(date, 5) -
        WEEK(DATE_SUB(date, INTERVAL DAYOFMONTH(date) - 1 DAY), 5) + 1) as week, date
    FROM myTable
    WHERE date BETWEEN start_date AND end_date
    ORDER BY week

アップデート2

SELECT  (WEEK(date, 1) -
        WEEK(DATE_SUB(date, INTERVAL DAYOFMONTH(date) - 1 DAY), 1) + 1) as week, date
    FROM myTable
    WHERE date BETWEEN start_date AND end_date
    ORDER BY week