A120122 -id:A120122

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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.

+10
2

1, 2, 64, 384, 139968

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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.

KEYWORD

base,nonn

AUTHOR

Farideh Firoozbakht, Aug 12 2006

STATUS

approved

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.

+10
2

1, 2, 672, 34992, 139968