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A038186
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Numbers divisible by the sum and product of their digits.
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15
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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
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OFFSET
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1,2
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COMMENTS
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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 Sándor, 2002. - Ctibor O. Zizka, Mar 04 2008
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a038186 n = a038186_list !! (n-1)
a038186_list = map succ $ elemIndices 1
$ zipWith (*) (map a188641 [1..]) (map a188642 [1..])
(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
(Python)
from math import prod
def sd(n): return sum(map(int, str(n)))
def pd(n): return prod(map(int, str(n)))
def ok(n): return n%sd(n) == 0 and pd(n) and n%pd(n) == 0
def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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