论文标题
关于素数和实际数字
On primes and practical numbers
论文作者
论文摘要
如果$ [1，n] $中的每个整数都作为$ n $的正分数的子集总和表示，则数字$ n $是实用的。我们考虑了实际数字的分布，这些数字也正在变化，从而改善了郭和温阿特纳的定理。此外，从本质上证明了玛根斯特恩的猜想，我们表明所有大数字都是素数和实用数字的总和。我们还考虑了用于实用数字的主要$ k $ tupers的类似物，证明了“正确”的上限，并且对成对，在梅尔菲的下限上有所改善。
A number $n$ is practical if every integer in $[1,n]$ can be expressed as a subset sum of the positive divisors of $n$. We consider the distribution of practical numbers that are also shifted primes, improving a theorem of Guo and Weingartner. In addition, essentially proving a conjecture of Margenstern, we show that all large odd numbers are the sum of a prime and a practical number. We also consider an analogue of the prime $k$-tuples conjecture for practical numbers, proving the "correct" upper bound, and for pairs, improving on a lower bound of Melfi.
