By Ayai Tomisawa TOKYO, Jan 21 (Reuters) - The Nikkei average gained 1 percent on Tuesday, recouping most of its losses suffered over the past three trading days, as investors bought back stocks on hopes that Japanese corporate earnings will be strong. The Nikkei ended 154.28 points higher at 15,795.96, recovering from a one-week low marked on Monday. The Topix added 0.2 percent to 1,295.95. The JPX-Nikkei Index 400, a recently introduced gauge comprised of firms with high return on equity and strong corporate governance, rose 0.2 percent to 11,701.46. A weaker yen lifted overall sentiment, prompting buying in such large-cap stocks as Fast Retailing Co and Toyota Motor Corp, which rose 2.9 percent and 1.5 percent, respectively.