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The Distribution of Values of the Divisor Function d(n)
Author(s) -
Erdos P.,
Mirsky L.
Publication year - 1952
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-2.1.257
Subject(s) - mathematics , combinatorics , distribution (mathematics) , function (biology) , citation , discrete mathematics , library science , computer science , biology , mathematical analysis , evolutionary biology
1. THROUGHOUT this note the letters p, q will be reserved for primes, and pV will denote the vth prime; cr, q,,... are to stand for absolute positive constants. Let d(n) denote, as usual, the number of positive divisors of n, and D(x) the number of distinct values assumed by d(n) in the range 1 < n < x. Our principal object is to estimate the order of magnitude of D(x) for large values of x. The argument will be based on a result concerning A-numbers, which are de&red as integers having the form