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Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem , there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes .
a superior highly composite number has a ratio between its number of divisors and itself raised to some positive power ... 200 1 deficient, prime 200: 1, 2, 4, 5, 8 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Since this is also a multiple of 4 for k > 0, 2 4k ±1 ≡ ±12 (mod 20). Thus, all Mersenne numbers M 4k +1 are congruent to 11 modulo 20 and end in 11, 31, 51, 71 or 91, while Mersenne numbers M 4k −1 ≡ 7 (mod 20) and end in 07, 27, 47, 67, or 87. For the perfect numbers, define P n = 2 n−1 M n be the value which is perfect if M n is prime.
Thus the "order of magnitude" of a number (on a larger scale than usually meant), can be characterized by the number of times (n) one has to take the to get a number between 1 and 10. Thus, the number is between 10 ↑ ↑ n {\displaystyle 10\uparrow \uparrow n} and 10 ↑ ↑ ( n + 1 ) {\displaystyle 10\uparrow \uparrow (n+1)} .
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The number appears in the Padovan sequence, preceded by 86, 114, 151 (it is the sum of the first two of these). [1] The sum of Euler's totient function φ(x) over the first twenty-five integers is 200. 200 is the smallest base 10 unprimeable number – it cannot be turned into a prime number by changing just one of its digits to any other digit.