# Efficient counting of Egyptian fractions with bounded denominators

I was amazed to discover that sequence http://oeis.org/A020473 in the OEIS has almost four hundred terms computed.

I wonder how one can get that far? E.g., how one can compute A020473(100)?

P.S. There was a related question Diophantine equation: Egyptian fraction representations of 1 about Egyptian fractions with a fixed number of reciprocals (with unbounded denominators) for which there seemed to be no efficient counting algorithm (to compute hundreds of terms) known. I found it interesting how complexity of these two problems differ.

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