reserve k,n,m,l,p for Nat;
reserve n0,m0 for non zero Nat;
reserve f for FinSequence;
reserve x,X,Y for set;
reserve f1,f2,f3 for FinSequence of REAL;
reserve n1,n2,m1,m2 for Nat;
reserve I,j for set;
reserve f,g for Function of I, NAT;
reserve J,K for finite Subset of I;

theorem Th36:
  Sigma(k) is multiplicative
proof
  for n being non zero Nat holds (Sigma k).n = Sum((EXP k)|
  NatDivisors n)
  proof
    let n be non zero Nat;
    thus (Sigma k).n = sigma(k,n) by Def3
      .= Sum((EXP k)|NatDivisors n) by Def2;
  end;
  hence Sigma(k) is multiplicative by Th34,Th35;
end;
