I followed TPH's advice and see what I got.

Let .

I divide the set of n in two parts:

One is of the form 7k-4 and second the rest.

For the first form, you can directly check by substituting the general form 7a-4 for n.

Now the second case.

We could see that also satisfy the given condition.

Now,

If you substitute the value of k=1,2,4,5,6,7 you get that are not divisible by 7.

Continuing this , now you can substitute the value k=8,9,11,12,13,14 and you get the non-divisibility of next six(out of seven, one you have alredy proved) by 7.

In this way you can complete the proof by mathamatical induction.

Bye.