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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). m is smoother than n if the largest prime factor of m is below the largest of n.
List Number of problems Number unsolved or incompletely solved Proposed by Proposed in Hilbert's problems [1] 23: 15: David Hilbert: 1900 Landau's problems [2] 4: 4: Edmund Landau: 1912 Taniyama's problems [3] 36 – Yutaka Taniyama: 1955 Thurston's 24 questions [4] [5] 24 – William Thurston: 1982 Smale's problems: 18: 14: Stephen Smale: 1998 ...
The sum of its factors (including one and itself) sum to 360, exactly three times 120. Perfect numbers are order two ( 2-perfect ) by the same definition. 120 is the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of two (8 + 16 + 32 + 64), and four consecutive powers ...
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In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 7 1, 9 = 3 2 and 64 = 2 6 are prime powers, while 6 = 2 × 3, 12 = 2 2 × 3 and 36 = 6 2 = 2 2 × 3 2 are not. The sequence of prime powers begins:
10 is square-free, as its divisors greater than 1 are 2, 5, and 10, none of which is square (the first few squares being 1, 4, 9, and 16) Square-free integers up to 120 remain after eliminating multiples of squares of primes up to √120. In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square ...
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The RSME actively collaborates with other scientific societies in Spain in various activities such as the celebration, in 2000, of the World Year of Mathematics, the preparation of the Spanish candidacy and the subsequent organization of the International Congress of Mathematicians (ICM) that was held in August 2006 in Madrid and the work of the Senate Report on the teaching of science in ...