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It means that 1, 4, and 36 are the only square highly composite numbers. Saying that the sequence of exponents is non-increasing is equivalent to saying that a highly composite number is a product of primorials or, alternatively, the smallest number for its prime signature .
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.
[48] The Euclidean algorithm was the first integer relation algorithm , which is a method for finding integer relations between commensurate real numbers. Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.W. Forcade (1979) [ 49 ] and the LLL algorithm .
These Calculators Make Quick Work of Standard Math, Accounting Problems, and Complex Equations Stephen Slaybaugh, Danny Perez, Alex Rennie May 21, 2024 at 2:44 PM
Note that the product need not be computed indefinitely, because if > then () =, so the product to calculate () can be terminated once . Also note that in the definition of e p ( x ) {\displaystyle e_{p}(x)} , 1 / x {\displaystyle 1/x} is analogous to ε {\displaystyle \varepsilon } in the implicit definition of a superior highly composite number.
The first: 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100 (sequence A001597 in the OEIS). 1 is sometimes included. A powerful number (also called squareful ) has multiplicity above 1 for all prime factors.
Animation showing an application of the Euclidean algorithm to find the greatest common divisor of 62 and 36, which is 2. A more efficient method is the Euclidean algorithm, a variant in which the difference of the two numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder) of a by b.
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