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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
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 ...
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.
The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal reciprocals of primes, factors of repunits, and lastly the prime factorization and the values of the functions φ ...
In Manam, the primary factor for using the paucal is not a specific number range, but the referents forming a single group; although the paucal is most common between 3 and 5, it has been used with more than 20. [83]
In the SVG file, hover over a bar to see its statistics. Roughly speaking, for a number to be highly composite it has to have prime factors as small as possible, but not too many of the same. By the fundamental theorem of arithmetic , every positive integer n has a unique prime factorization: