Let me make an educated guess here based on the graphical capabilities in FLOPS based on very unreliable sources:

The PS1 has a 33mhz GPU - (32-bit R800A), that we would assume as a single core. The PS4 has a 1ghz AMD HD 7670 GPU (assisted by A10 APU).

According to GameSpot you can calculate the amount of FLOPS for a GPU by applying the basic formula:

(# of parallel GPU processing cores multiplied by peak clock speed in MHz multiplied by two) divided by 1,000,000 (to make it tera)

Assuming the PS1 would have 1 GPU processing core, multiplied by the peak clock speed of 33mhz, multiplied by 2, divided by 1.000.000.

(1*33*2)/1.000.000 = 0,000066 teraFLOPS

The PS4 has 1,843 teraFLOPS according to the GameSpot source mentioned earlier.

Calculating the amount of PS1's needed to provide the same graphical processing power as the PS4, it would come down to:

1,832/0,000066 = 27757,57 PS1's

1 PS4 ≈ 27758 PS1's