This is a problem I had a look at some years ago but always had the feeling that I was missing something behind its motivation.

D.H. Lehmer says in his 1947 paper, “The Vanishing of Ramanujan's Function τ(n),” that it is natural to ask whether τ(n)=0 for any n>0.

My question is: Why is it natural to wonder whether τ(n)=0 any n>0?

Are there any particular arithmetic properties among the many satisfied  by τ(n) that would lead one to ponder its vanishing? The problem is mentioned [here][taufunction], where it's stated that it was a conjecture of Lehmer, although it's not actually presented as a conjecture in his paper, more a curiosity.

Maybe there is no deep reason to ponder the vanishing of τ(n), in which case that would be a satisfactory answer too. 

 
[taufunction]: http://mathworld.wolfram.com/TauFunction.html