A120121 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.

1, 2, 64, 384, 139968

Offset

1,2

Comments

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).

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Crossrefs

Cf. A120122, A120123.

Sequence in context: A120829 A226397 A264481 * A274656 A298276 A299369

Adjacent sequences: A120118 A120119 A120120 * A120122 A120123 A120124

Keyword

base,nonn

Author

Farideh Firoozbakht, Aug 12 2006

Status

approved