how to count amount of numbers of a power number

[onnix]

I have a power number ((a^b)^c)^d. I want to know how many number will be produced if the terms a,b,c,d will run from 1 to n. Can anyone help me a general formula to calculate myself, or a result with n, say, 16?

Thanks.

 

[Deleted member 4993]

I have a power number ((a^b)^c)^d. I want to know how many number will be produced if the terms a,b,c,d will run from 1 to n. Can anyone help me a general formula to calculate myself, or a result with n, say, 16?

Thanks.

Suppose you restricted the values (of a,b,c &d) to only 2 numbers (1 & 2) - how many numbers can you generate?

Suppose you restricted the values (of a,b,c &d) to only 2 numbers (2 & 3) - how many numbers can you generate?

 

[Dr.Peterson]

I have a power number ((a^b)^c)^d. I want to know how many number will be produced if the terms a,b,c,d will run from 1 to n. Can anyone help me a general formula to calculate myself, or a result with n, say, 16?

Have you observed that you can simplify ((a^b)^c)^d ? It's not the same as a^(b^(c^d)).

It's not hard to count the number of possible lists (a, b, c, d). The hard part will be to eliminate duplicate values.

What is the context of your question? Is it for a course, or just curiosity, or for some actual purpose? That might affect how hard I'd be willing to work on it, and what kind of help I'd offer.