Try doing this:
week_grouped = df.groupby('week')
week_grouped.sum().reset_index().to_csv('week_grouped.csv')
That’ll write the entire dataframe to the file. If you only want those two columns then,
week_grouped = df.groupby('week')
week_grouped.sum().reset_index()[['week', 'count']].to_csv('week_grouped.csv')
Here’s a line by line explanation of the original code:
# This creates a "groupby" object (not a dataframe object)
# and you store it in the week_grouped variable.
week_grouped = df.groupby('week')
# This instructs pandas to sum up all the numeric type columns in each
# group. This returns a dataframe where each row is the sum of the
# group's numeric columns. You're not storing this dataframe in your
# example.
week_grouped.sum()
# Here you're calling the to_csv method on a groupby object... but
# that object type doesn't have that method. Dataframes have that method.
# So we should store the previous line's result (a dataframe) into a variable
# and then call its to_csv method.
week_grouped.to_csv('week_grouped.csv')
# Like this:
summed_weeks = week_grouped.sum()
summed_weeks.to_csv('...')
# Or with less typing simply
week_grouped.sum().to_csv('...')