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A034838 Numbers n that are divisible by every digit of n. 30
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; text; internal format)
OFFSET

1,2

COMMENTS

Subset of zeroless numbers A052382: Integers with at least one digit 0 (A011540) are excluded.

A128635(a(n)) = n.

Contains in particular all repdigits A010785 \ {0}. - M. F. Hasler, Jan 05 2020

REFERENCES

Charles Ashbacher, Journal of Recreational Mathematics, Vol. 33 (2005), pp. 227. See problem number 2693.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit

Index entries for 10-automatic sequences.

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.

64 is not included because even though 4 divides 64, 6 does not.

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); # Emeric Deutsch

MATHEMATICA

divByEvryDigitQ[n_] := Block[{id = Union[IntegerDigits[n]]}, Union[ IntegerQ[ #] & /@ (n/id)] == {True}]; Select[ Range[ 487],  divByEvryDigitQ[#] &] (* Robert G. Wilson v, Jun 21 2005 *)

Select[Range[500], FreeQ[IntegerDigits[#], 0]&&AllTrue[#/ IntegerDigits[ #], IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 31 2019 *)

PROG

(Haskell)

a034838 n = a034838_list !! (n-1)

a034838_list = filter f a052382_list where

   f u = g u where

     g v = v == 0 || mod u d == 0 && g v' where (v', d) = divMod v 10

-- Reinhard Zumkeller, Jun 15 2012, Dec 21 2011

(PARI) is(n)=my(v=vecsort(eval(Vec(Str(n))), , 8)); if(v[1]==0, return(0)); for(i=1, #v, if(n%v[i], return(0))); 1 \\ Charles R Greathouse IV, Apr 17 2012

(PARI) is_A034838(n)=my(d=Set(digits(n))); d[1]&&!forstep(i=#d, 1, -1, n%d[i]&&return) \\ M. F. Hasler, Jan 10 2016

(Python)

A034838_list = []

for g in range(1, 4):

    for n in product('123456789', repeat=g):

        s = ''.join(n)

        m = int(s)

        if not any(m % int(d) for d in s):

            A034838_list.append(m) # Chai Wah Wu, Sep 18 2014

(Python)

for n in range(10**3):

    s = str(n)

    if '0' not in s:

        c = 0

        for i in s:

            if n%int(i):

                c += 1

                break

        if not c:

            print(n, end=', ') # Derek Orr, Sep 19 2014

(MAGMA) [n:n in [1..500]| not 0 in Intseq(n) and #[c:c in [1..#Intseq(n)]| n mod Intseq(n)[c] eq 0] eq #Intseq(n)] // Marius A. Burtea, Sep 12 2019

CROSSREFS

Intersection of A002796 (numbers divisible by each nonzero digit) and A052382 (zeroless numbers), or A002796 \ A011540 (numbers with digit 0).

Subsequence of A034709 (divisible by last digit).

Contains A007602 (multiples of the product of their digits) and subset A059405 (n is the product of its digits raised to positive powers), A225299 (divisible by square of each digit), and A066484 (n and its rotations are divisible by each digit).

Sequence in context: A084434 A034709 A178158 * A063527 A209933 A182183

Adjacent sequences:  A034835 A034836 A034837 * A034839 A034840 A034841

KEYWORD

nonn,base,nice

AUTHOR

Erich Friedman

STATUS

approved

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Last modified November 29 04:03 EST 2020. Contains 338756 sequences. (Running on oeis4.)