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Extreme values for divisor functions

Published online by Cambridge University Press:  17 April 2009

R.A. MacLeod
R.A. MacLeod
Affiliation:
Department of Mathematics, University of Victoria, P.O. Box 1700, Victoria, B.C., Canada V8W 2Y2
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Abstract

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Maximum and minimum values are obtained for some sums invovling the divisor functions of number theory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 447 - 465
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bottroff, G.A., ‘On divisor sums’ Indian J. Pure Appl. Math. 2 (1971), 501–503.Google Scholar
[2]MacLeod, R.A., ‘The minimum of φ(x)/x 2’, J. London Math. Soc. 42 (1967), 652–660.CrossRefGoogle Scholar
[3]MacLeod, R.A., ‘A new estimate for the sum of ’, Acta Arithmetica 13 (1967), 49–59.CrossRefGoogle Scholar
[4]MacLeod, R.A., ‘Fractional part sums and divisor functions’, J. Number Theory 14 (1982), 185–227.CrossRefGoogle Scholar
[5]Rogers, K., ‘The Schnirelmann density of the squarefree integers’, Proc. Amer. Math. Soc. 15 (1964), 515–516.Google Scholar
[6]Walfisz, A., Weylsche Exponentialsummen in der neuren Zahlentheorie XV, VEB, Mathematische Forschungsberichte (Duetscher Verlag der Wissenschaften, Berlin, 1963).Google Scholar