%I #3 Mar 30 2012 17:37:44

%S 1,2,64,384,139968

%N Numbers n such that n=phi((d_1*d_2*...*d_k)*(d_1+d_2+...+d_k)) where d_1 d_2... d_k is the decimal expansion of n.

%C Conjecture: 139968 is the largest term. Except for the first term all terms are even. It's interesting that for the number 139968 we have the following relations: 139968=phi((1*3*9*9*6*8)*(1+3+9+9+6+8))=phi(1*3*9*9*6*8) *(1+3+9+9+6+8)=(1*3*9*9*6*8)*phi(1+3+9+9+6+8).

%e 384 is in the sequence because 384=phi((3*8*4)*(3+8+4)).

%t Do[If[h = IntegerDigits[n]; l = Length[h]; EulerPhi[ Product[h[[k]], {k, l}]*Sum[h[[k]], {k, l}]] == n, Print[n]], {n, 100000000}]

%Y Cf. A120122, A120123.

%K base,nonn

%O 1,2

%A _Farideh Firoozbakht_, Aug 12 2006