A246757 Largest n-digit number divisible by the product of its decimal digits.

9, 36, 816, 9612, 93744, 973728, 9939915, 99221112, 997711344, 9993393711, 99934212672, 999641938176, 9999121936392, 99996414731136, 999994123418112, 9999982411646976, 99999318116613312, 999991631331122112, 9999944111773994112, 99999911232931433472, 999999832211912282112

Offset: 1

Author

Max Alekseyev, Sep 02 2014

Keywords

• nonn
• base

Comments

The smallest such numbers are given by repunits A000042 or A002275.

Links

• Max Alekseyev, Table of n, a(n) for n = 1..30

Crossrefs

Subsequence of A007602.

Programs

PARI

{ A246757(n) = my(m,d,p,q); m=n\2; forstep(k=10^m-1,(10^m-1)/9,-1, d=digits(k); q=prod(i=1,#d,d[i]); if(q==0,next); forstep(s=(((k+1)*10^(n-m))\q)*q,k*10^(n-m),-q,  d=digits(s); p=prod(i=1,#d,d[i]); if(p==0 || s%p,next); return(s) )) }

Python

from operator import mul
from functools import reduce
def A246757(n):
    for i in range(10**n-1,int('1'*n)-1,-1):
        pd = reduce(mul,(int(d) for d in str(i)))
        if pd and not i % pd:
            return i # Chai Wah Wu, Sep 08 2014