The maximum number of baskets is the largest divisor of N not exceeding (1 + sqrt(1 + 8N))/2.
Gardner,The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications, Copernicus (Springer)
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The Apple Pear Basket Problem: A Combinatorial Exploration
The maximum number of baskets is the largest divisor of N not exceeding (1 + sqrt(1 + 8N))/2.