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A034838
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Numbers n that are divisible by every digit of n.
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13
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 111, 112, 115, 122, 124, 126, 128, 132, 135, 144, 155, 162, 168, 175, 184, 212, 216, 222, 224, 244, 248, 264, 288, 312, 315, 324, 333, 336, 366, 384, 396, 412, 424, 432, 444, 448
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Integers with at least one 0 digit are excluded.
A128635(a(n)) = n.
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REFERENCES
| Charles Ashbacher, Journal of Recreational Mathematics, Vol. 33 (2005), pp. 227. See problem number 2693.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| 36 is in the sequence because it is divisible by both 3 and 6.
48 is included because both 4 and 8 divide 48.
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MAPLE
| a:=proc(n) local nn, j, b, bb: nn:=convert(n, base, 10): for j from 1 to nops(nn) do b[j]:=n/nn[j] od: bb:=[seq(b[j], j=1..nops(nn))]: if map(floor, bb)=bb then n else fi end: 1, 2, 3, 4, 5, 6, 7, 8, 9, seq(seq(seq(a(100*m+10*n+k), k=1..9), n=1..9), m=0..6); (Deutsch)
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MATHEMATICA
| fQ[n_] := Block[{id = Union[IntegerDigits[n]]}, Union[ IntegerQ[ # ] & /@ (n/id)] == {True}]; Select[ Range[ 487], fQ[ # ] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 21 2005)
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PROG
| (Haskell)
import Data.List (unfoldr)
a034838 n = a034838_list !! (n-1)
a034838_list = filter f a052382_list where
f x = all (== 0) $ map (x `mod`) $ unfoldr
(\z -> if z == 0 then Nothing else Just $ swap $ divMod z 10) x
-- Reinhard Zumkeller, Dec 21 2011
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CROSSREFS
| Cf. A002706, A034709, A007602.
Cf. A052382.
Sequence in context: A084434 A034709 A178158 * A063527 A064700 A180484
Adjacent sequences: A034835 A034836 A034837 * A034839 A034840 A034841
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KEYWORD
| nonn,base,nice
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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