cp's OEIS Frontend

A002796 Numbers that are divisible by each nonzero digit.

%I A002796 M0474 N0175 #69 Sep 08 2022 08:44:31
%S A002796 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,
%T A002796 70,77,80,88,90,99,100,101,102,104,105,110,111,112,115,120,122,124,
%U A002796 126,128,132,135,140,144,150,155,162,168,175,184,200,202,204,208,210,212
%N A002796 Numbers that are divisible by each nonzero digit.
%C A002796 If n is a member so is 10*n. Also all repunits are members. - _Robert G. Wilson v_, Apr 12 2015
%C A002796 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
%C A002796 The number of terms < 10^k: 9, 32, 137, 751, 4577, 29950, 207197, 1495637, ... . - _Robert G. Wilson v_, Apr 13 2015
%C A002796 Includes all multiples of 2520. - _Robert Israel_, Apr 15 2015
%C A002796 For n >= 10: A067458(a(n)) = 0. - _Reinhard Zumkeller_, Sep 24 2015
%D A002796 Lindon, Visible factor numbers, J. Rec. Math., 1 (1968), 217.
%D A002796 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002796 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002796 T. D. Noe, <a href="/A002796/b002796.txt">Table of n, a(n) for n = 1..2000</a>
%H A002796 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A002796 a(n) ~ 2520*n. - _Charles R Greathouse IV_, Feb 13 2017
%p A002796 select(t -> t mod ilcm(op(convert(convert(t,base,10),set) minus {0})) = 0, [$1..1000]); # _Robert Israel_, Apr 15 2015
%t A002796 dQ[n_]:=Module[{nzidn=DeleteCases[IntegerDigits[n],0]},And@@Divisible[n, nzidn]]; Select[Range[250],dQ] (* _Harvey P. Dale_, Dec 13 2011 *)
%o A002796 (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
%o A002796 (Haskell)
%o A002796 import Data.List (nub, sort); import Data.Char (digitToInt)
%o A002796 a002796 n = a002796_list !! (n-1)
%o A002796 a002796_list = filter f [1..] where
%o A002796    f x = all ((== 0) . mod x) ds where
%o A002796      ds = map digitToInt (if c == '0' then cs else cs')
%o A002796      cs'@(c:cs) = nub $ sort $ show x
%o A002796 -- _Reinhard Zumkeller_, Jan 01 2014
%o A002796 (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
%o A002796 (Python)
%o A002796 A002796_list = []
%o A002796 for i in range(1,10**5):
%o A002796     for d in set(str(i)):
%o A002796         if d != '0' and i % int(d):
%o A002796             break
%o A002796     else:
%o A002796         A002796_list.append(i) # _Chai Wah Wu_, Mar 26 2021
%Y A002796 Cf. A007602, A034838, A237851.
%Y A002796 Cf. A171492 (complement).
%Y A002796 Cf. A067458.
%K A002796 nonn,base,easy,nice
%O A002796 1,2
%A A002796 _N. J. A. Sloane_
%E A002796 More terms from _Henry Bottomley_, Jun 06 2000