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132 is the sixth Catalan number. [1] With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136. [2]132 is an oblong number, as the product of 11 and 12 [3] whose sum instead yields the 9th prime number 23; [4] on the other hand, 132 is the 99th composite number.
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. ... 132: 2 2 ·3 ...
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
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:
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133 is an n whose divisors (excluding n itself) added up divide φ().It is an octagonal number [1] and a happy number. [2]133 is a Harshad number, because it is divisible by the sum of its digits.
In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby (little omega) counts each distinct prime factor, whereas the related function () (big omega) counts the total number of prime factors of , honoring their multiplicity (see arithmetic function).
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.