### List Tutorial Exercise 5

The obvious first step is to obtain the list of factors with k f. This list will always be in sorted order, so if there are duplicates they will be right next to each other. A suitable method is to compare the list with a copy of itself shifted over by one.

1:  [3, 7, 7, 7, 19]   2:  [3, 7, 7, 7, 19]     2:  [3, 7, 7, 7, 19, 0]
.                  1:  [3, 7, 7, 7, 19, 0]  1:  [0, 3, 7, 7, 7, 19]
.                        .

19551 k f              RET 0 |                  TAB 0 TAB |



1:  [0, 0, 1, 1, 0, 0]   1:  2          1:  0
.                        .              .

V M a =                  V R +          0 a =


Note that we have to arrange for both vectors to have the same length so that the mapping operation works; no prime factor will ever be zero, so adding zeros on the left and right is safe. From then on the job is pretty straightforward.

Incidentally, Calc provides the @c{\dfn{M\"obius} $\mu$} Moebius mu function which is zero if and only if its argument is square-free. It would be a much more convenient way to do the above test in practice.