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

1,1

Comments

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

Links

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

Prog

(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

Crossrefs

Subsequence of A007602.

Sequence in context: A223306 A272890 A129425 * A079655 A203764 A053949

Adjacent sequences: A246754 A246755 A246756 * A246758 A246759 A246760

Keyword

nonn,base

Author

Max Alekseyev, Sep 02 2014

Status

approved