Related but not strong enough. 17 x 17 x 17 = 4,913 is 2^8-smooth - no prime factors larger than 2^8 - and it is less than 2^16, but 17 x 17 = 289 does not fit into a byte. Smoothness is required but not sufficient for a product representation to exist.

It's related, but not the same thing. For example, for b=10, the number 70=2x5x7 is b-smooth, but it cannot be written as the product of two numbers less than b. Here are the other b-smooth (counter)examples for b=10:

    | n   | factorization  | products of two numbers
    |-----|----------------|------------------------------------
    | 50  | 2 * 5^2        | 1x50, 2x25, 5x10
    | 60  | 2^2 * 3 * 5    | 1x60, 2x30, 3x20, 4x15, 5x12, 6x10
    | 70  | 2 * 5 * 7      | 1x70, 2x35, 5x14, 7x10
    | 75  | 3 * 5^2        | 1x75, 3x25, 5x15
    | 80  | 2^4 * 5        | 1x80, 2x40, 4x20, 5x16, 8x10
    | 84  | 2^2 * 3 * 7    | 1x84, 2x42, 3x28, 4x21, 6x14, 7x12
    | 90  | 2 * 3^2 * 5    | 1x90, 2x45, 3x30, 5x18, 6x15, 9x10
    | 96  | 2^5 * 3        | 1x96, 2x48, 3x32, 4x24, 6x16, 8x12
    | 98  | 2 * 7^2        | 1x98, 2x49, 7x14