divisors
start with a cube then add consecutive primes
b Divisors(b) relevant expression
0 3 3^3
1 7 3^3*5
2 15 3^3*5*7
3 31 3^3*5*7*11
q(0) = 3
q(b) = 2*q(b-1) + 1
just like before
because of the way prime numbers work under this count divisors function,
the primes could be any primes, not neccessarily consecutive, and
the count would be the same.
For example, for relavent expression 7^3, we still have q(0) = 3
My guess is that for any p^3, we have q(0) = 3.
By guess I mean infer from observed patterns.
There is no textbook titled 'observational number theory'.
However 'Computational Number Theory' by Pomerance and Crandall is at
least 300 pages of good fun. To be honest, my copy is nowhere to be found.
Away from keyboard soon. Matt