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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. ... 126: 2·3 2 ...
[1] [2] 126 is a sum of two cubes, and since 125 + 1 is σ 3 (5), 126 is the fifth value of the sum of cubed divisors function. [3] [4] 126 is the fifth -perfect Granville number, and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such ...
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 ...
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.
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
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.
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125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur. Like many other powers of 5, it is a Friedman number in base 10 since 125 = 5 1 + 2. 125 is the center of a close triplet of perfect powers, (121 = 11 2, 125 = 5 3, 128 = 2 7). Excluding the trivial cases of 0 and 1 ...