WASHINGTON—U.S. manufacturing activity picked up further in September, but factories experienced longer delays getting raw materials delivered and paid higher prices for inputs. The Institute for Supply Management (ISM) said on Friday its index of national factory activity increased to a reading of 61.1 last month from 59.9 in August. A reading above 50 indicates expansion in manufacturing, which accounts for 12 percent of the U.S. economy. Economists polled by Reuters had forecast the index falling to 59.6. Some of the surprise rise in the ISM index, however, was due to a jump in the survey’s measure of supplier deliveries to a reading of 73.4 last month from 69.5 in August. A reading above 50 percent indicates slower deliveries, but a lengthening in suppliers’ delivery times is normally associated with a strong economy and increased customer demand, which would be a positive contribution to the ISM index. But in this …