Postgres 13

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CREATE TABLE eddi_minute (serialno serial, "timestamp" timestamp);
INSERT INTO eddi_minute ("timestamp") VALUES (generate_series(now() - interval '1 year', now(), '1 minute'));
525601 rows affected

CREATE INDEX idx_ts ON eddi_minute (date_part('week', "timestamp"));
CREATE INDEX idx_timestamp ON eddi_minute ("timestamp");
EXPLAIN (ANALYSE,COSTS OFF)
SELECT date_part('week', "timestamp") , count(DISTINCT serialno) 
FROM eddi_minute em 
GROUP BY date_part('week', "timestamp")  

QUERY PLAN

GroupAggregate (actual time=5.558..277.689 rows=53 loops=1)

  Group Key: date_part('week'::text, "timestamp")

  ->  Index Scan using idx_ts on eddi_minute em (actual time=0.064..216.788 rows=525601 loops=1)

Planning Time: 0.510 ms

Execution Time: 277.864 ms

EXPLAIN (ANALYSE,COSTS OFF)
select count(distinct serialno) as Devices
from eddi_minute em where "timestamp" >= '2021-06-23 00:01:00' and "timestamp" < '2021-06-23 00:02:00';

QUERY PLAN

Aggregate (actual time=0.043..0.044 rows=1 loops=1)

  ->  Bitmap Heap Scan on eddi_minute em (actual time=0.036..0.037 rows=1 loops=1)

        Recheck Cond: (("timestamp" >= '2021-06-23 00:01:00'::timestamp without time zone) AND ("timestamp" < '2021-06-23 00:02:00'::timestamp without time zone))

        Heap Blocks: exact=1

        ->  Bitmap Index Scan on idx_timestamp (actual time=0.026..0.026 rows=1 loops=1)

              Index Cond: (("timestamp" >= '2021-06-23 00:01:00'::timestamp without time zone) AND ("timestamp" < '2021-06-23 00:02:00'::timestamp without time zone))

Planning Time: 0.141 ms

Execution Time: 0.077 ms