On Sequences of Positive Integers

نویسندگان

  • H. DAVENPORT
  • P. ERDÖS
چکیده

where [a, b, . . .] denotes the least common multiple of a, b, . . . . For the first term above represents the density of the multiples of a1 , the second represents the density of those multiples of a 2 that are not multiples of a 1 , and so on . Now suppose we start from an infinite sequence a,, a2 , . . . (arranged in increasing order) instead of from a finite set . It is plain that A(ai, a2 , . . . , a m) increases with m, and is always less than i . We define A = lim A (a,, a,, . . , am) . ( .2 )

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تاریخ انتشار 1937