A120123 - OEIS

A120123

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

1, 2, 672, 34992, 139968

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OFFSET

1,2

COMMENTS

Conjecture: 139968 is the largest term. Except for the first term, all terms are even. 139968 is also in A120121 & A120122, so it has a very pleasant property (see the Comments lines of A120121).

LINKS

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

Prime Curios, 139968.

EXAMPLE

34992 is in the sequence because 34992=(3*4*9*9*2)*phi(3+4+9+9+2).

MATHEMATICA

Do[If[h = IntegerDigits[n]; l = Length[h]; n == Product[h[[k]], {k, l}]*EulerPhi[Sum[h[[k]], {k, l}]], Print[n]], {n, 50000000}]

CROSSREFS

Cf. A120121, A120122.

Sequence in context: A156938 A285221 A079195 * A140014 A188698 A209364

Adjacent sequences: A120120 A120121 A120122 * A120124 A120125 A120126

KEYWORD

base,nonn

AUTHOR

Farideh Firoozbakht, Aug 12 2006

STATUS

approved