Let σ(n) be the sum of the positive divisors of

  1. Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $10$ positive divisors, and $mn$
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  2. A positive integer is called nice if it is a multiple of $8.$A certain nice positive integer $n$ has exactly $9$ positive
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  3. Find the smallest number N such that:The number of divisors of N is A. The number of divisors of A is B. The number of divisors
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  4. the only perfect number of the form x(n) + y(n)A perfect number is an integer that is equal to the sum of its positive divisors
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  5. The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$What is the smallest positive integer that
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  6. If positive integer number n has exactly 8 divisors, what is the least number of divisors can n2 have?
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  7. Let f:ℤ+ → ℤ+ be the function defined by: for each x ∈ ℤ+, f(x) is the number of positive divisors of x.- find
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  8. Let f:ℤ+ → ℤ+ be the function defined by: for each x ∈ ℤ+, f(x) is the number of positive divisors of x.- find
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  9. Let f:ℤ+ → ℤ+ be the function defined by: for each x ∈ ℤ+, f(x) is the number of positive divisors of x.- find
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  10. For how many odd positive integers n<1000 does the number of positive divisors of n divide n?
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