Problem 52804. Easy Sequences 29: Odd proper divisors of odd proper divisors
The number
is special. It has odd number of proper divisors:
. Furthermore, if you take any of its proper divisors, say
, it too has odd number of proper divisors:
. The numbers
and
, have similar property as
.
Given a limit n, find how many integers
, have similar property as 210, namely, the integers should have odd number of proper divisors and all its proper divisors have odd number of proper divisors, as well.
The number
, does not qualify because it has even proper divisors, 8 in total
. The number
also doesn't qualify because although it has
proper divisors, some of its divisor, like
, have even number of proper divisors.
NOTE: A proper divisor of a number, is a divisor which is less than the number. Exception to this rule is the number 1, which is considered a proper divisor of itself.
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