(* The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 -> 363601 -> 1454 -> 169
871 -> 45361 -> 871
872 -> 45362 -> 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 -> 363600 -> 1454 -> 169 -> 363601 (-> 1454)
78 -> 45360 -> 871 -> 45361 (-> 871)
540 -> 145 (-> 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
*) 

let rec fact x =
    if( x<2 ) then 1 else
    x*(fact (x-1))
;;

let rec digits x =
    if( x<10 ) then [x] else
    (x mod 10)::(digits (x/10))
;;

(* sum of digits factorials *)
let sodf x = List.fold_left (+) 0 (List.map fact (digits x));;

let search =
    (* number of unique terms, <=60 *)
    let rec len x i l =
        if(i>60) then 0 else 
        if(List.mem x l) then i else
        len (sodf x) (i+1) (x::l)
    in
    let rec search x n =
        if(x>999999) then n else
        search (x+1) (if( (len x 0 []) = 60 ) then (n+1) else n)
    in
        search 1 0
;;

Printf.printf "%d\n" search;