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The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 135: 3 3 ·5 ...
If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
The factorizations are often not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one. The entry 4+2i = −i(1+i) 2 (2+i), for example, could also be written as 4+2i= (1+i) 2 (1−2i). The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right ...
135 Hertha is a large main belt asteroid which orbits among the Nysa asteroid family. 135 film, the cartridge version of 35mm photographic film, used widely in still photography. The Canon FD 135 mm lens. In astrology, when two planets are 135 degrees apart, they are in an astrological aspect called a sesquiquadrate.
a factor of 10001 (the other being 73) and the repdigit 11111111 (= 10001 × 1111). using two radii to divide a circle according to the golden ratio yields sectors of approximately 137.51° (the golden angle ) and 222 ° in degree system so 137 is the largest integer before it.
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The ρ algorithm was a good choice for F 8 because the prime factor p = 1238926361552897 is much smaller than the other ... American Mathematical Society. pp. 135–138.