Hostile Divisor Numbers
Some divisors of positive integers really hate each other and they don't like to share one or more common digits.
For example the number
9566
has 4 divisors:
1, 2, 4783 and 9566
(as you can see,
no two of them share the same digit
).
Thus,
9566
is a
H
ostile
D
ivisor
N
umber (
HDN
) but
9567 is NOT
because its divisors (1, 3, 9, 1063, 3189, 9567) share some common digits.
There are
26 HDN
under
100
:
1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 27, 29, 37, 43, 47, 49, 53, 59, 67, 73, 79, 83, 86, 87, 89, 97
How many HDN are there under 1,000,000 ?
The answer is 34607.
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