A288069 - OEIS

A288069

Quotients obtained when the Zuckerman numbers are divided by the product of their digits.

1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 3, 3, 2, 111, 56, 23, 8, 22, 9, 9, 5, 53, 18, 14, 52, 21, 4, 18, 51, 13, 8, 7, 17, 1111, 556, 371, 223, 186, 377, 28, 37, 19, 303, 12, 437, 74, 28, 59, 9, 49, 528, 67, 93, 27, 1037, 174, 22, 151, 13, 184, 29, 514, 66, 46

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

COMMENTS

The Zuckerman numbers (A007602) are the numbers that are divisible by the product of their digits.

Question: Is A067251 a subsequence? No, it appears in A056770 that not all integers other than multiples of 10 can be obtained as quotient, such as 15, 16, 24, 25, 26, 32, .... (see A342941).

The limit of the sequence is infinite: for any x, there is some N such that, for all n > N, a(n) > x. Proof: a Zuckerman number with d digits is at least 10^(d-1) and has a digit product at most 9^d and so has a quotient at least 10^(d-1)/9^d which goes to infinity with d. - Charles R Greathouse IV, Jun 05 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(11) = 12/(1*2) = 6; a(13) = 24/(2*4) = 3.

MAPLE

f:= proc(n) local L, p;

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

if p > 0 then

if n mod p = 0 then return n/p fi

end proc:

map(f, [$1..10^4]); # Robert Israel, Jun 05 2017

MATHEMATICA