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The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd. A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct
Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful. The following is a list of all powerful numbers between 1 and 1000:
This is a list of articles about prime numbers. 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.
Klauber's 1932 paper describes a triangle in which row n contains the numbers (n − 1) 2 + 1 through n 2. As in the Ulam spiral, quadratic polynomials generate numbers that lie in straight lines. Vertical lines correspond to numbers of the form k 2 − k + M. Vertical and diagonal lines with a high density of prime numbers are evident in the ...
In number theory, a weird number is a natural number that is abundant but not semiperfect. [ 1 ] [ 2 ] In other words, the sum of the proper divisors ( divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.
1 1–1000. 2 1001–2000. 3 2001–3000. 4 3001–4000. 5 4001–5000. 6 5001–6000. 7 6001–7000. ... This is a list of all articles about natural numbers from 1 ...
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).
In number theory, a Descartes number is an odd number which would have been an odd perfect number if one of its composite factors were prime.They are named after René Descartes who observed that the number D = 3 2 ⋅7 2 ⋅11 2 ⋅13 2 ⋅22021 = (3⋅1001) 2 ⋅ (22⋅1001 − 1) = 198585576189 would be an odd perfect number if only 22021 were a prime number, since the sum-of-divisors ...
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