What the following number Sequence

[a2m7l5]

1244
114448
12818176
205090816
_____________
what the following number

 

[Dragonfall]

1729

 

[njama]

$$2^2 \cdot 311 \cdot 1$$

$$2^2 \cdot 311 \cdot 23 \cdot 2^2$$

$$2^2 \cdot 311 \cdot 23 \cdot 7 \cdot 2^2 \cdot 2^4$$

$$2^2 \cdot 311 \cdot 23 \cdot 7 \cdot 2^2 \cdot 2^4 \cdot 2^4$$

 

[a2m7l5]

where the Responses

 

[Dragonfall]

where the Responses

1729

...

 

[njama]

And why do you think it is 1729?

 

[Dragonfall]

Obviously it's the fifth value of the function f:N->N which is 0 everywhere except for 1 through 5, which have the values (resp.) 1244, 114448, 12818176, 205090816 and 1729.