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A038186 Numbers divisible by the sum and product of their digits. 11
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; text; internal format)
OFFSET

1,2

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, Mar 04 2008

A188641(a(n)) * A188642(a(n)) = 1: intersection of A005349 and A007602. [Reinhard Zumkeller, Apr 07 2011]

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

J. Sandor, Geometric Theorems, Diophantine Equations and Arithmetic Functions. American Research Press, Rehoboth 2002.

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, Feb 12 2008

MATHEMATICA

dspQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Times@@idn; t!=0 && Divisible[n, Total[idn]] && Divisible[n, t]]; Select[Range[11500], dspQ] (* Harvey P. Dale, Jul 11 2011 *)

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

(PARI) for(n=1, 10^4, d=digits(n); s=sumdigits(n); p=prod(i=1, #d, d[i]); if(p&&!(n%s+n%p), print1(n, ", "))) \\ Derek Orr, Apr 29 2015

CROSSREFS

Cf. A005349, A007602.

Sequence in context: A001102 A051004 A032575 * A118575 A165307 A081549

Adjacent sequences:  A038183 A038184 A038185 * A038187 A038188 A038189

KEYWORD

nonn,base,nice,look

AUTHOR

Felice Russo

EXTENSIONS

More terms from Patrick De Geest, Jun 15 1999

STATUS

approved

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Last modified June 24 05:50 EDT 2017. Contains 288697 sequences.