A002796 - OEIS

A002796

Numbers that are divisible by each nonzero digit.
(Formerly M0474 N0175)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

FORMULA

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

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 *)

PROG

(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

-- 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

(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

CROSSREFS

Cf. A007602, A034838, A237851.

Cf. A171492 (complement).

Cf. A067458.