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Old 2021-06-14, 01:28   #1
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"Matthew Anderson"
Dec 2010
Oregon, USA

2×3×151 Posts
Default [found it] want curve fit

I have a question for all you mathematics and computer programming experts.

Note that the 'proper divisors' of a positive integers
are the divisors of that integer including one and excluding the integer itself.

We want to find patterns in the ProperDivisors() function.

count of Proper Divisors
any single prime has a single proper divisor and it is one.

b [count of proper Divisors(b)] relavent expression

0 2 p0^2
1 5 p0^2*p1
2 11 p0^2*P1*p2
3 23 p0^2*p1*p2*p3
4 47 p0^2*p1*p2*p3*p4
5 143 ----------------------- p0^2*p1*p2*p3*p4*p5 so 3^2*5*7*11*13*17
6 191
7 383

this last data point is more than a one hundred second calculation.

What is the curve fit expression for this dateset?


Last fiddled with by retina on 2021-06-14 at 14:04 Reason: Letting everyone know your found it
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Old 2021-06-14, 01:32   #2
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"Matthew Anderson"
Dec 2010
Oregon, USA

38A16 Posts

Nevermind. I got it.

b(n) = 2*b(n-1) + 1.

Not easy.

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