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A288069 Quotients obtained when the Zuckerman numbers are divided by the product of their digits. 11
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
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
Sequence in context: A359439 A359492 A347357 * A236175 A193813 A338920
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jun 05 2017
STATUS
approved

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Last modified March 28 21:56 EDT 2024. Contains 371254 sequences. (Running on oeis4.)