Summing in Mathematica.

[MathematicalPhysicist]

I want to write down summation of the type
$$\sum_{d|n , d<n}$$ or $$\sum_{d|n}$$ both summing over d.
and d|n means d divides n.

I know that I can use Sum[term, {i, n-1}] but I don't know how to use this condition of divisibility to the summation.
any help?

Thanks.

 

[EnumaElish]

You need to define term as a function of d and n such that "term = 0 unless d|n." Look into modulus arithmetic commands.

 

[Bill Simpson]

In[1]:= n=12; Sum[If[Mod[n,d]==0,a^d,0],{d,n-1}]

Out[1]= a + a^2 + a^3 + a^4 + a^6