Achilles number

A powerful number that is not a perfect power. If

n = \prod_{i} p_{i}^{e_{i}}

is its prime factorization, the conditions are

e_{i} \geq 2

for every

i

and

g cd (e_{1}, \dots, e_{k}) = 1

.

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- Strong Achilles number Achilles number

Strong Achilles number

n

for which both

n

and its Euler totient

φ (n)

are Achilles numbers.

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Strong Achilles number

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Achilles number by

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An Achilles number is a positive integer that is a powerful number but not a perfect power. A powerful number is defined as a number \( n \) such that in its prime factorization, every prime number \( p \) appears with an exponent of at least 2. In contrast, a perfect power is a number of the form \( m^k \) where \( m \) and \( k \) are positive integers and \( k \geq 2 \).

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