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.

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

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

Harvey P. Dale, Table of n, a(n) for n = 1..179

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

Sequence in context: A232709 A249334 A338257 * A064702 A034710 A305257

Adjacent sequences: A064155 A064156 A064157 * A064159 A064160 A064161

Keyword

easy,nonn,base

Author

Felice Russo, Sep 14 2001

Extensions

More terms from Jason Earls, Dec 04 2001

Status

approved