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

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

Mathematica

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

Crossrefs

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

Sequence in context: A359439 A359492 A347357 * A236175 A193813 A338920

Adjacent sequences: A288066 A288067 A288068 * A288070 A288071 A288072

Keyword

nonn,base

Author

Bernard Schott, Jun 05 2017

Status

approved