A002796 Numbers that are divisible by each nonzero digit.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

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

Includes all multiples of 2520. - Robert Israel, Apr 15 2015

For n >= 10: A067458(a(n)) = 0. - Reinhard Zumkeller, Sep 24 2015

References

• 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).

Links

• T. D. Noe, Table of n, a(n) for n = 1..2000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A007602, A034838, A237851.

Cf. A171492 (complement).

Cf. A067458.

Programs

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
-- Reinhard Zumkeller, Jan 01 2014

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

Maple

select(t -> t mod ilcm(op(convert(convert(t,base,10),set) minus {0})) = 0, [$1..1000]); # Robert Israel, Apr 15 2015

Mathematica

dQ[n_]:=Module[{nzidn=DeleteCases[IntegerDigits[n],0]},And@@Divisible[n, nzidn]]; Select[Range[250],dQ] (* Harvey P. Dale, Dec 13 2011 *)

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

Python

A002796_list = []
for i in range(1,10**5):
    for d in set(str(i)):
        if d != '0' and i % int(d):
            break
    else:
        A002796_list.append(i) # Chai Wah Wu, Mar 26 2021

Formula

a(n) ~ 2520*n. - Charles R Greathouse IV, Feb 13 2017

Extensions

More terms from Henry Bottomley, Jun 06 2000