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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 54: 2·3 3: ...
54 is an abundant number and a semiperfect number, like all other multiples of 6. [1] It is twice the third power of three, 3 3 + 3 3 = 54, and hence is a Leyland ...
2.54 Repunit primes. ... (or prime) is a natural number ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is ...
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...
The challenge was to find the prime factors of each number. ... As of February 2020, the smallest 23 of the 54 listed numbers have been factored.
If all the prime factors of a number are repeated it is called a powerful number (All perfect powers are powerful numbers). If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7 ...
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It is the only number in the Mersenne sequence whose prime factors are each factors of at least one previous element of the sequence (3 and 7, respectively the first and second Mersenne primes). [7] In the list of Mersenne numbers, 63 lies between Mersenne primes 31 and 127, with 127 the thirty-first prime number. [5]