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A002796
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Numbers that are divisible by each nonzero digit.
(Formerly M0474 N0175)
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16
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 22, 24, 30, 33, 36, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 102, 104, 105, 110, 111, 112, 115, 120, 122, 124, 126, 128, 132, 135, 140, 144, 150, 155, 162, 168, 175, 184, 200, 202, 204, 208, 210, 212
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OFFSET
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1,2
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COMMENTS
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If n is a member so is 10*n. Also all repunits are members. - Robert G. Wilson v, Apr 12 2015
The repdigits are also members because they're always the repunit number of the same length multiplied by the digit being repeated. - Eric Fox, Sep 02 2019
The number of terms < 10^k: 9, 32, 137, 751, 4577, 29950, 207197, 1495637, ... . - Robert G. Wilson v, Apr 13 2015
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REFERENCES
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Lindon, Visible factor numbers, J. Rec. Math., 1 (1968), 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MAPLE
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select(t -> t mod ilcm(op(convert(convert(t, base, 10), set) minus {0})) = 0, [$1..1000]); # Robert Israel, Apr 15 2015
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MATHEMATICA
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dQ[n_]:=Module[{nzidn=DeleteCases[IntegerDigits[n], 0]}, And@@Divisible[n, nzidn]]; Select[Range[250], dQ] (* Harvey P. Dale, Dec 13 2011 *)
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PROG
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(PARI) is(n)=my(v=vecsort(eval(Vec(Str(n))), , 8)); for(i=1+(v[1]==0), #v, if(n%v[i], return(0))); 1 \\ Charles R Greathouse IV, Apr 17 2012
(Haskell)
import Data.List (nub, sort); import Data.Char (digitToInt)
a002796 n = a002796_list !! (n-1)
a002796_list = filter f [1..] where
f x = all ((== 0) . mod x) ds where
ds = map digitToInt (if c == '0' then cs else cs')
cs'@(c:cs) = nub $ sort $ show x
(Magma) sol:=[]; for k in [1..220] do a:=Set(Intseq(k)) diff {0}; if #[c:c in a|IsIntegral(k/c)] eq #a then; Append(~sol, k); end if; end for; sol; // Marius A. Burtea, Sep 09 2019
(Python)
for i in range(1, 10**5):
for d in set(str(i)):
if d != '0' and i % int(d):
break
else:
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CROSSREFS
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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