* Japan's factory activity grows at slowest pace in 7 months - PMI
* S.Korea activity increases but optimism dented - survey
* Fallout from China's slowdown seen weighing on Asian economies

Asia's manufacturing activity broadly stagnated in September as pandemic-induced factory shutdowns and signs of slowing Chinese growth weighed on the region's economies, surveys showed on Friday.
Countries where large outbreaks of the Delta variant receded saw an improvement in activity, such as Indonesia and India.
But factory activity in September shrank in Malaysia and Vietnam, and grew in Japan at the slowest rate in seven months, as chip shortages and supply disruptions added to the woes of a region still struggling to shake off the hit from Covid-19.
China's waning economic momentum dealt a fresh blow to the region's growth prospects, with the official Purchasing Manager's Index (PMI) on Thursday showing the country's factory activity unexpectedly shrank in September due to wider curbs on electricity use.
While the private Caixin/Markit Manufacturing PMI fared better than expected after slumping in August, growing signs of weakness in the world's second-largest economy are clouding the outlook for neighbouring Asian countries.
"While coronavirus curbs on economic activity may be gradually lifted, the slow pace at which this will happen means Southeast Asian economies will stagnate for the rest of this year," said Makoto Saito, an economist at NLI Research Institute.
The final au Jibun Bank Japan Manufacturing PMI slipped to 51.5 in September from 52.7 in the previous month, marking its slowest pace of expansion since February.
Manufacturers in the world's third-largest economy faced pressure from pandemic restrictions and heightened supply chain disruptions as well as shortages of raw materials and delivery delays.
South Korea's PMI for September rose to 52.4 from 51.2 in August, helped by an expansion in production and new orders.
It stayed above the 50-mark threshold that indicates expansion in activity for a 12th straight month, but continued supply chain disruptions dented business optimism for manufacturers.
Taiwan's factory activity continued to expand but at its slowest pace in over a year.
Taiwan's PMI index eased to 54.7 in September from 58.5 in August, while Vietnam saw the index unchanged from August at 40.2.
In a glimmer of hope, the PMI for Indonesia rose to 52.2 from 43.7 in August, while that for India improved to 53.7 in September from 52.3 in the previous month.
"While regional PMIs showed that the disruption from large virus waves in the region is easing somewhat, unmet orders continue to pile up, meaning that the resulting shortages further down supply chains are set to remain for some time to come," said Alex Holmes, emerging Asia economist at Capital Economics.
Once seen as a driver of global growth, Asia's emerging economies are lagging advanced economies in recovering from the pandemic's pain as delays in vaccine rollouts and a spike in Delta variant cases hurt consumption and factory production.