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A038186
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Numbers divisible by the sum and product of their digits.
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7
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1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 111, 112, 132, 135, 144, 216, 224, 312, 315, 432, 612, 624, 735, 1116, 1212, 1296, 1332, 1344, 1416, 2112, 2232, 2916, 3132, 3168, 3276, 3312, 4112, 4224, 6624, 6912, 8112, 9612, 11112, 11115, 11133, 11172, 11232
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The property "numbers divisible by the sum and product of their digits" leads to the Diophantine equation t*x1*x2*...*xr=s*(x1+x2+...+xr), where t and s are divisors of n; xi is from [1...9]. This corresponds to some arithmetic problems in geometry, see Sandor, 2002. - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 04 2008
A188641(a(n)) * A188642(a(n)) = 1: intersection of A005349 and A007602. [Reinhard Zumkeller, Apr 07 2011]
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REFERENCES
| J. Sandor, Geometric Theorems, Diophantine Equations and Arithmetic Functions. American Research Press, Rehoboth 2002. http://www.gallup.unm.edu/~smarandache/JozsefSandor2.pdf
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MAPLE
| P:=proc(n) local i, k, w, x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=1; k:=i; while k>0 do x:=x*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if x>0 then if i/x=trunc(i/x) and i/w=trunc(i/w) then print(i); fi; fi; od; end: P(1000); - Paolo P. Lava (paoloplava(AT)gmail.com), Feb 12 2008
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MATHEMATICA
| dspQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Times@@idn; t!=0 && Divisible[n, Total[idn]] && Divisible[n, t]]; Select[Range[11500], dspQ] (* From Harvey P. Dale, Jul 11 2011 *)
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PROG
| (Haskell)
import Data.List (elemIndices)
a038186 n = a038186_list !! (n-1)
a038186_list = map succ $ elemIndices 1
$ zipWith (*) (map a188641 [1..]) (map a188642 [1..])
-- Reinhard Zumkeller, Apr 07 2011
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CROSSREFS
| Cf. A005349, A007602.
Sequence in context: A001102 A051004 A032575 * A118575 A165307 A081549
Adjacent sequences: A038183 A038184 A038185 * A038187 A038188 A038189
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KEYWORD
| nonn,base,nice
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AUTHOR
| Felice Russo (frusso(AT)micron.com)
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1999.
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