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A034710
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Positive numbers for which the sum of digits equals the product of digits.
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14
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1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 132, 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, 12221, 12511
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Positive numbers n such that A007953(n) = A007954(n).
If n is a member, the digits of n are solutions of the equation x1*x2*...*xr = x1+x2+...+xr ; xi are from [1...9]. Permutations of digits (x1,...,xr) are different numbers n with the same property S(n)=PI(n). For example : x1*x2=x1+x2 this equation has only 1 solution (2,2) which gives the number 22. x1*x2*x3=x1+x2+x3 has a solution (1,2,3), so numbers 123,132,213,231,312,321 has the property. - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 04 2008
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1200
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EXAMPLE
| 1124 is a member since 1+1+2+4 = 1*1*2*4 = 8.
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MATHEMATICA
| Select[Range[12512], (Plus @@ IntegerDigits[ # ]) == (Times @@ IntegerDigits[ # ]) &] (Alonso Delarte (alonso.delarte(AT)gmail.com), May 16 2005)
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PROG
| (Haskell)
import Data.List (elemIndices)
a034710 n = a034710_list !! (n-1)
a034710_list = elemIndices 0 $ map (\x -> a007953 x - a007954 x) [1..]
-- Reinhard Zumkeller, Mar 19 2011
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CROSSREFS
| Cf. A061672.
Sequence in context: A110002 A064158 A064702 * A061672 A132080 A048386
Adjacent sequences: A034707 A034708 A034709 * A034711 A034712 A034713
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KEYWORD
| nonn,base,nice,easy
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
| Corrected by Larry Reeves (larryr(AT)acm.org), Jun 27 2001
Definition changed by N. J. A. Sloane (njas(AT)research.att.com) to specifically exclude 0, Sep 22 2007
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