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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. ... 84: 2 2 ·3 ...
The number of divisors of 84 is 12. [6] As no smaller number has more than 12 divisors, 84 is a largely composite number. [7] The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits. [8]
A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3, 5, 7, 11, 13, 17, 19, 23, ... (OEIS: A038134) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: 2, 97, 127, 149, 191, 211, 223, 227, 229, 251.
84 24 25200 4,2,2,1 9 ... Roughly speaking, for a number to be highly composite it has to have prime factors as small as possible, but not too many of the same.
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 ...
All prime numbers are known to be solitary, as are powers of prime numbers. More generally, if the numbers n and σ( n ) are coprime – meaning that the greatest common divisor of these numbers is 1, so that σ( n )/ n is an irreducible fraction – then the number n is solitary (sequence A014567 in the OEIS ).
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The numbers which remain prime under cyclic shifts of digits. A016114: Home prime: 1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... For n ≥ 2, a(n) is the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached; a(n) = −1 if no prime is ever reached. A037274