%I #32 Aug 16 2021 15:51:49

%S 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,

%T 18,51,13,8,7,17,1111,556,371,223,186,377,28,37,19,303,12,437,74,28,

%U 59,9,49,528,67,93,27,1037,174,22,151,13,184,29,514,66,46

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

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

%C 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).

%C 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

%H Charles R Greathouse IV, <a href="/A288069/b288069.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%p if p > 0 then

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

%p fi

%p end proc:

%p map(f, [$1..10^4]); # _Robert Israel_, Jun 05 2017

%t Select[Table[n/Max[Times@@IntegerDigits[n],Pi/100],{n,5000}],IntegerQ] (* _Harvey P. Dale_, Aug 16 2021 *)

%Y Cf. A007602, A067251, A056770, A342593, A342941.

%K nonn,base

%O 1,10

%A _Bernard Schott_, Jun 05 2017