I'm not quite sure why my code gives 52 as the answer for: weekofyear("01/JAN/2017") .  
Does anyone have a possible explanation for this? Is there a better way to do this?
from pyspark.sql import SparkSession, functions
spark = SparkSession.builder.appName('weekOfYear').getOrCreate()
from pyspark.sql.functions import to_date
df = spark.createDataFrame(
    [(1, "01/JAN/2017"), (2, "15/FEB/2017")], ("id", "date")) 
df.show()
+---+-----------+
| id|       date|
+---+-----------+
|  1|01/JAN/2017|
|  2|15/FEB/2017|
+---+-----------+
Calculate the week of the year
df=df.withColumn("weekofyear", functions.weekofyear(to_date(df["date"],"dd/MMM/yyyy")))
df.printSchema()
root
 |-- id: long (nullable = true)
 |-- date: string (nullable = true)
 |-- weekofyear: integer (nullable = true)
df.show()
The 'error' is visible below:
+---+-----------+----------+
| id|       date|weekofyear|
+---+-----------+----------+
|  1|01/JAN/2017|        52|
|  2|15/FEB/2017|         7|
+---+-----------+----------+
It seems like weekofyear() will only return 1 for January 1st if the day of the week is Monday through Thursday.
To confirm, I created a DataFrame with all "01/JAN/YYYY" from 1900 to 2018:
df = sqlCtx.createDataFrame(
    [(1, "01/JAN/{y}".format(y=year),) for year in range(1900,2019)],
    ["id", "date"]
)
Now let's convert it to a date, get the day of the week, and count the values for weekofyear():
import pyspark.sql.functions as f
df.withColumn("d", f.to_date(f.from_unixtime(f.unix_timestamp('date', "dd/MMM/yyyy"))))\
    .withColumn("weekofyear", f.weekofyear("d"))\
    .withColumn("dayofweek", f.date_format("d", "E"))\
    .groupBy("dayofweek", "weekofyear")\
    .count()\
    .show()
#+---------+----------+-----+
#|dayofweek|weekofyear|count|
#+---------+----------+-----+
#|      Sun|        52|   17|
#|      Mon|         1|   18|
#|      Tue|         1|   17|
#|      Wed|         1|   17|
#|      Thu|         1|   17|
#|      Fri|        53|   17|
#|      Sat|        53|    4|
#|      Sat|        52|   12|
#+---------+----------+-----+
Note, I am using Spark v 2.1 where to_date() does not accept a format argument, so I had to use the method described in this answer to convert the string to a date.
Similarly to_date() only returns 1 for:
Update
This behavior is consistent with the ISO 8601 definition.
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