A120122 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, 24, 139968

Offset

1,2

Comments

Conjecture: 139968 is the largest term. Except for the first term all terms are even. 139968 is also in the sequences A120121 & A120123, so it has a very pleasant property (see the Comments lines of A120121).

Links

Table of n, a(n) for n=1..4.

Prime Curios, 139968.

Example

24 is in the sequence because 24=phi(2*4)*(2+4).

Mathematica

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

Crossrefs

Cf. A120121, A120123.

Sequence in context: A098679 A123851 A258824 * A068943 A100815 A365617

Adjacent sequences: A120119 A120120 A120121 * A120123 A120124 A120125

Keyword

base,fini,nonn

Author

Farideh Firoozbakht, Aug 12 2006

Status

approved