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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
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
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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23- titlePerfect Power -- from Wolfram MathWorld
- DC.TitlePerfect Power
- DC.CreatorWeisstein, Eric W.
- DC.DescriptionA 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,...
- descriptionA 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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- og:titlePerfect Power -- from Wolfram MathWorld
- og:descriptionA 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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- twitter:titlePerfect Power -- from Wolfram MathWorld
- twitter:descriptionA 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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49- http://oeis.org/A001597
- http://oeis.org/A070428
- http://oeis.org/A072102
- http://oeis.org/A072103
- http://oeis.org/A117453