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A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
The number 28 depicted as 28 balls arranged in a triangular pattern with the number of layers of 7 28 as the sum of four nonzero squares. Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: 1 + 2 + 4 + 7 + 14 = 28 {\displaystyle 1+2+4+7+14=28} .
In 1747, Leonhard Euler completed what is now called the Euclid–Euler theorem, showing that these are the only even perfect numbers. As a result, there is a one-to-one correspondence between Mersenne primes and even perfect numbers, so a list of one can be converted into a list of the other. [1] [5] [6]
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.
Powerball winning numbers for 12/28/2024. The winning numbers for the Powerball drawing on Saturday, Dec. 28 are 6, 31, 51, 54 and 55.The red Powerball was 12, and the Power Play was 2X.
The sum of positive divisors function σ z (n), for a real or complex number z, is defined as the sum of the zth powers of the positive divisors of n.It can be expressed in sigma notation as