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Search: id:A120121
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| A120121 |
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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. |
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3
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OFFSET
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1,2
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COMMENT
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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).
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EXAMPLE
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384 is in the sequence because 384=phi((3*8*4)*(3+8+4)).
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MATHEMATICA
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Do[If[h = IntegerDigits[n]; l = Length[h]; EulerPhi[ Product[h[[k]], {k, l}]*Sum[h[[k]], {k, l}]] == n, Print[n]], {n, 100000000}]
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CROSSREFS
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Cf. A120122, A120123.
Sequence in context: A004853 A064010 A120829 this_sequence A047707 A134939 A122603
Adjacent sequences: A120118 A120119 A120120 this_sequence A120122 A120123 A120124
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KEYWORD
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base,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 12 2006
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