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.
d [count of proper Divisors(d)] relavent expression
n b(n)
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 hundread second calculation.
What is the curve fit expression for this dataset?
Regards,
Matt
(i asked mersennefourm.com)
but then I realized -
so b(n) = 2*b(n-1) + 1.
Induction by Matt.