• Ensure that the default statistics gathering program is configured and Running.

  SELECT STATUS 
  FROM DBA_AUTOTASK_CLIENT 
  WHERE CLIENT_NAME='auto optimizer stats collection';
  

• Ensure that the default statistics gathering program is configured to run only on weekends.

BEGIN
DBMS_AUTO_TASK_ADMIN.ENABLE(
 CLIENT_NAME => 'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'SATURDAY_WINDOW');
DBMS_AUTO_TASK_ADMIN.ENABLE(
 CLIENT_NAME => 'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'SUNDAY_WINDOW');
END;
/

/* End of Script */

• Default schedule is daily. So disable the daily schedules for optimizer statistics.

  /* Start of Script – Script to be executed as SYS*/

BEGIN
DBMS_AUTO_TASK_ADMIN.DISABLE(
 CLIENT_NAME => 'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'MONDAY_WINDOW');
DBMS_AUTO_TASK_ADMIN.DISABLE(
 CLIENT_NAME =>'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'TUESDAY_WINDOW');
DBMS_AUTO_TASK_ADMIN.DISABLE(
 CLIENT_NAME =>'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'WEDNESDAY_WINDOW');
DBMS_AUTO_TASK_ADMIN.DISABLE(
 CLIENT_NAME => 'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'THURSDAY_WINDOW');
DBMS_AUTO_TASK_ADMIN.DISABLE(
 CLIENT_NAME => 'auto optimizer stats collection', 
 OPERATION => NULL, 
 WINDOW_NAME => 'FRIDAY_WINDOW');
END;
/

SELECT WINDOW_NAME,OPTIMIZER_STATS
FROM DBA_AUTOTASK_WINDOW_CLIENTS;

Should return
MONDAY_WINDOW                   DISABLED
TUESDAY_WINDOW                   DISABLED
WEDNESDAY_WINDOW            DISABLED
THURSDAY_WINDOW                DISABLED
FRIDAY_WINDOW                      DISABLED
SATURDAY_WINDOW               ENABLED
SUNDAY_WINDOW                    ENABLED