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A007602 Numbers that are divisible by the product of their digits.
(Formerly M0482)
36
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 36, 111, 112, 115, 128, 132, 135, 144, 175, 212, 216, 224, 312, 315, 384, 432, 612, 624, 672, 735, 816, 1111, 1112, 1113, 1115, 1116, 1131, 1176, 1184, 1197, 1212, 1296, 1311, 1332, 1344, 1416, 1575, 1715, 2112, 2144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are called Zuckerman numbers to base 10. [Howard Berman (howard_berman(AT)hotmail.com), Nov 09 2008]

This sequence is a subsequence of A180484; the first member of A180484 that is not a member of A007602 is 1114. [D. S. McNeil, Sep 09 2010]

Complement of A188643; A188642(a(n)) = 1; A038186 is a subsequence; A168046(a(n)) = 1: subsequence of A052382. [Reinhard Zumkeller, Apr 07 2011]

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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

Index entries for Colombian or self numbers and related sequences

MAPLE

filter:= proc(n)

local p;

p:= convert(convert(n, base, 10), `*`);

p <> 0 and n mod p = 0

end proc;

select(filter, [$1..10000]); # Robert Israel, Aug 24 2014

MATHEMATICA

zuckerQ[n_] := Module[{d = IntegerDigits[n], prod}, prod = Times @@ d; prod > 0 && Mod[n, prod] == 0]; Select[Range[5000], zuckerQ] (* Alonso del Arte, Aug 04 2004 *)

PROG

(Haskell)

import Data.List (elemIndices)

a007602 n = a007602_list !! (n-1)

a007602_list = map succ $ elemIndices 1 $ map a188642 [1..]

-- Reinhard Zumkeller, Apr 07 2011

(MAGMA) [ n: n in [1..2144] | not IsZero(&*Intseq(n)) and IsZero(n mod &*Intseq(n)) ];  // Bruno Berselli, May 28 2011

(Python)

from operator import mul

from functools import reduce

A007602 = [n for n in range(1, 10**5) if not (str(n).count('0') or n % reduce(mul, (int(d) for d in str(n))))] # Chai Wah Wu, Aug 25 2014

(PARI)

for(n=1, 10^5, d=digits(n); p=prod(i=1, #d, d[i]); if(p&&n%p==0, print1(n, ", "))) \\ Derek Orr, Aug 25 2014

CROSSREFS

Cf. A002796, A034709, A034838.

Cf. A001103.

Sequence in context: A182183 A064700 A180484 * A167620 A169935 A193498

Adjacent sequences:  A007599 A007600 A007601 * A007603 A007604 A007605

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

STATUS

approved

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Last modified April 29 19:06 EDT 2017. Contains 285613 sequences.