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The multiplicity of a prime factor p of n is the largest exponent m for which p ... A Ruth-Aaron pair is two consecutive numbers ... 99: 3 2 ·11 100: 2 2 ·5 2: 101 ...
Two numbers with the same "abundancy" form a friendly pair; ... 99: 156: 52/33 100: 217: ... at least one of the prime factors must be congruent to 1 modulo 3 and ...
99 is: a composite number; a square-prime, of the form (p 2, q). It is the 11th composite number of this form and the third of the form (3 2, q). It has an aliquot sum of 57, within an aliquot sequence of two composite numbers (99,57,23,1,0), to the Prime in the 23-aliquot tree. a Kaprekar number [1] a lucky number; a palindromic number in base ten
n with an even number of distinct prime factors (μ(n)=1) 2 6 35 56 324 583 3383 6093 + + n with an odd number of distinct prime factors (μ(n)=-1) 4 6 32 64 351 617 3438 6067 + + n even with an odd number of prime factors 1 2 9 21 100 180 1010 6067 + + n even with an odd number of distinct prime factors 3 4 21 49 268 482 2486 4452 + +
More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...
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:
Our bodies have 3 billion genetic building blocks, or base pairs, that make us who we are. And of those 3 billion base pairs, only a tiny amount are unique to us, making us about 99.9% genetically ...
If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.