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A064158
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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.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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]
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..179
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EXAMPLE
| 22 belongs to the sequence because (2*2)^(2+2)=(2+2)^(2*2)
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MATHEMATICA
| okQ[n_]:=Module[{idn=IntegerDigits[n], t, p}, t= Times@@idn; p=Total[idn]; t^p==p^t]; Select[Range[12500], okQ]
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CROSSREFS
| Sequence in context: A045910 A128290 A110002 * A064702 A034710 A061672
Adjacent sequences: A064155 A064156 A064157 * A064159 A064160 A064161
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KEYWORD
| easy,nonn,base
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AUTHOR
| Felice Russo (frusso(AT)micron.com), Sep 14 2001
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Dec 04 2001
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