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Perfect Power -- from Wolfram MathWorld

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...



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Perfect Power -- from Wolfram MathWorld

https://mathworld.wolfram.com/PerfectPower.html

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...



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https://mathworld.wolfram.com/PerfectPower.html

Perfect Power -- from Wolfram MathWorld

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...

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      Perfect Power -- from Wolfram MathWorld
    • DC.Title
      Perfect Power
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      A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...
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      A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...
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      Perfect Power -- from Wolfram MathWorld
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      A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...
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      A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a perfect power iff GCD(a_1,a_2,...,a_k)>1. Including duplications (i.e., taking all numbers up to some cutoff and taking all their powers) and taking m>1, the first few are 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, ... (OEIS A072103). Here, 16 is duplicated since 16=2^4=4^2. (1) As shown by Goldbach,...
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