Euler's totient function computes the sum +/1=n+.i.n ,  the number of numbers less than n which are relatively prime to n . If

is the prime factorization of n where the are distinct primes, then

The formula readily translates into J,

totient=: (- ~:)&.q:

noting that q:^:_1 is */ .

   totient 28
12
+/ 1 = 28 +. i.28
12

totient 1
1
totient 7
6
totient !40x
121343746763281707274905415180804423680000000000

x=: 637 274
+./ x
1
*/ totient x
68544
totient */ x
68544

In J6.01, the totient function can also be computed by 5 p: y . Thus:

   5 p: !40x
121343746763281707274905415180804423680000000000

The totient function can also be computed as * -.@%@~.&.q: ; the present simpler definition is due to AndrewNikitin as posted to the J Forum on 2009-11-03.