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m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
162 (one hundred [and] sixty-two) is the natural number between 161 and 163. In mathematics. Having only 2 and 3 as its prime divisors, 162 is a 3-smooth number.
The sum of an integer's unique factors, up to n=2000. ... 162: 81/53 107: 108: 108/107 ... the "primitive" friendly pair 6 and 28 gives rise to friendly pairs 6n and ...
Any Ruth–Aaron pair of square-free integers belongs to both lists with the same sum of prime factors. The intersection also contains pairs that are not square-free, for example (7129199, 7129200) = (7×11 2 ×19×443, 2 4 ×3×5 2 ×13×457).
If all e i ≡ 1 (mod 3) or 2 (mod 5), then the smallest prime factor of N must lie between 10 8 and 10 1000. [41] More generally, if all 2e i +1 have a prime factor in a given finite set S, then the smallest prime factor of N must be smaller than an effectively computable constant depending only on S. [41]
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
The only prime belonging to two pairs of cousin primes is 7. One of the numbers n, n + 4, n + 8 will always be divisible by 3, so n = 3 is the only case where all three are primes. An example of a large proven cousin prime pair is (p, p + 4) for = + which has 20008 digits.
If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.