7973

7973 is a natural number that comes after 7972 and before 7974. It is an odd composite number with a prime factorization of 7 × 17 × 67, which makes it square-free. Because it is a product of three distinct primes, its positive divisors are 1, 7, 17, 67, 119, 469, 1139, and 7973, giving it eight divisors in total. Consequently, 7973 is not a prime, nor a perfect square or cube. In modular arithmetic, 7973 is congruent to 0 modulo 7, 8 modulo 9, and 1 modulo 4. In binary notation, 7973 is 1101100111101₂.

From a number-theoretic perspective, the square-free nature implies that its Möbius function μ(7973) equals −1, since it has an odd number (three) of distinct prime factors. The sum of its digits is 26, so it is not divisible by 3 and is not a Harshad number.

Beyond pure mathematics, 7973 can appear as an identifier in catalogs, problem sets, or numerical sequences where integers are listed sequentially. However, there is no widely recognized meaning or name attached to 7973 beyond its numerical properties.

In summary, 7973 is an odd, square-free composite number with a clear prime factorization, a distinct set of divisors, and straightforward residue properties in several bases, illustrating typical aspects of a specific integer within number theory.

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