Conway-Sloane Powertrain, other than in base 10

[Jonathan Post]

Conway-Sloane Powertrain, other than in base 10.

Base 2:

0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, ...

Base 3:

0, 1, 2, 1, 1, 1, 1, 2, 4, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 2,
4, 0, 4, 8, 1

I'd like to see the array A[k,n] powertrain of base-k expression for n.

Row 10 = A133500.

Row 1 = 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

Row 2 and 3 start as above.

Example:

A[3,26] = 8 because A007089(26) = 222, and (2^2)*2 = 8.

Of course, there is an implicit binary structure in Conway's definition:

abcd... is the decimal expression of a number n, then the powertrain
of n is the number n' = a^b*c^d*

The ternary would be:

abcdefghi... is the decimal expression of a number n, then the
triple-geared-powertrain of n is the number
n' = (a^b^c) * (d^e^f) * (g^h^i) * ...

Best,

Jonathan Vos Post