Abstract
A number theoretic function f(n) is called multiplicative if f(ab) = f(a)f(b) for (a, b) = 1, it is called additive if f(a b) = f(a) + f(b) for (a, b) = 1. A function f(n) is said to have a distribution function if for every c the density g(c) of integers satisfying f(n) < c exists and g(— ∞) = 0, g(∞) = 1. In this note we give some best possible estimates for g(c + 1/t) - g(t), for the case of f(n) = σ(n)/n.
Original language | English |
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Pages (from-to) | 59-65 |
Number of pages | 7 |
Journal | Pacific Journal of Mathematics |
Volume | 52 |
Issue number | 1 |
Publication status | Published - 1974 |
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ASJC Scopus subject areas
- Mathematics(all)
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On the distribution of numbers of the form σ(N)/n and on some related questions. / Erdős, P.
In: Pacific Journal of Mathematics, Vol. 52, No. 1, 1974, p. 59-65.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the distribution of numbers of the form σ(N)/n and on some related questions
AU - Erdős, P.
PY - 1974
Y1 - 1974
N2 - A number theoretic function f(n) is called multiplicative if f(ab) = f(a)f(b) for (a, b) = 1, it is called additive if f(a b) = f(a) + f(b) for (a, b) = 1. A function f(n) is said to have a distribution function if for every c the density g(c) of integers satisfying f(n) < c exists and g(— ∞) = 0, g(∞) = 1. In this note we give some best possible estimates for g(c + 1/t) - g(t), for the case of f(n) = σ(n)/n.
AB - A number theoretic function f(n) is called multiplicative if f(ab) = f(a)f(b) for (a, b) = 1, it is called additive if f(a b) = f(a) + f(b) for (a, b) = 1. A function f(n) is said to have a distribution function if for every c the density g(c) of integers satisfying f(n) < c exists and g(— ∞) = 0, g(∞) = 1. In this note we give some best possible estimates for g(c + 1/t) - g(t), for the case of f(n) = σ(n)/n.
UR - http://www.scopus.com/inward/record.url?scp=33745678591&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745678591&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:33745678591
VL - 52
SP - 59
EP - 65
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 1
ER -