"Group By " index usage

I have a table with this index:

create index ARTISTS_NAME on ARTISTS (
lower(AR_NAME)
);

Te index is over a colum with this definition:

AR_NAME VARCHAR(256) null,

I want to optimize this query:

select * from artists where lower(ar_name) like
lower('a%') order by lower(ar_name) limit 20;

I think the planner should use the index i have. But
the result of the explain command is:

explain analyze select * from artists where
lower(ar_name) like lower('a%') order by
lower(ar_name) limit 20;

QUERY PLAN
------------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=20420.09..20420.14 rows=20 width=360)
(actual time=2094.13..2094.19 rows=20 loops=1)
-> Sort (cost=20420.09..20433.52 rows=5374
width=360) (actual time=2094.13..2094.16 rows=21
loops=1)
Sort Key: lower((ar_name)::text)
-> Index Scan using artists_name on artists
(cost=0.00..19567.09 rows=5374 width=360) (actual
time=0.11..1391.97 rows=59047 loops=1)
Index Cond: ((lower((ar_name)::text) >=
'a'::text) AND (lower((ar_name)::text) < 'b'::text))
Filter: (lower((ar_name)::text) ~~
'a%'::text)
Total runtime: 2098.62 msec
(7 rows)

The "ORDER BY" clause is not using the index!. I don't
know why.

I have the locale configured to C, and the index works
well with the "like" operator.

¿Could you help me? I am really lost.

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