

A064158


Integers n such that (x1*x2*..xk)^(x1+x2+..xk) = (x1+x2+..xk)^(x1*x2*...xk) where x1x2..xk are the digits of n in base 10.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 112, 121, 123, 132, 211, 213, 231, 312, 321, 1124, 1142, 1214, 1241, 1412, 1421, 2114, 2141, 2411, 4112, 4121, 4211, 11125, 11133, 11152, 11215, 11222, 11251, 11313, 11331, 11512, 11521, 12115, 12122, 12151, 12212
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OFFSET

1,2


COMMENTS

With the exception of only 112,121, and 211, each term of this sequence satisfies (sum of digits) equals (product of digits). For 112, 121, and 211, the sum of the digits is 4, the product of the digits is 2, and the terms qualify because 2^4 equals 4^2. [From Harvey P. Dale, Sep 30 2011]


LINKS



EXAMPLE

22 belongs to the sequence because (2*2)^(2+2)=(2+2)^(2*2)


MATHEMATICA

okQ[n_]:=Module[{idn=IntegerDigits[n], t, p}, t= Times@@idn; p=Total[idn]; t^p==p^t]; Select[Range[12500], okQ]


CROSSREFS



KEYWORD

easy,nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



