What is the size of the kth Superabundant Number?

Asked Jul 19 '19 at 15:06

Active Jul 19 '19 at 20:05

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Utilizing the data generated by T.D. Noe for the first $10^6$ terms of A004394, a plot of $k$ against $log_{10}(S(k))$ where S(K) is the $k^{th}$ Superabundant Number shows a strong linear relationship which suggests the following:

$$S(k)\approx e^{0.242692k}$$

Is this a known result and does this relationship hold past $k=10^6$? Can the exact value of the constant be determined?

edited Jul 19 '19 at 20:05

asked Jul 19 '19 at 15:06

Goldbug

1,024

Linking to another question where I use this result. – Goldbug Jul 19 '19 at 15:42
Briggs shows a similar result for the density of SAs but not clear how they are related. See Figure 2. – Goldbug Jul 19 '19 at 15:46

What is the size of the kth Superabundant Number?

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