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An Analogue of a Result of Jacobsthal

Published online by Cambridge University Press:  20 January 2009

Eckford Cohen
Eckford Cohen
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee, U.S.A.
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Jacobsthal (4)has proved that the n×n matrix

is invertible with the inverse,

Here μ(x) denotes the Möbius function for positive integral x and is assumed to be 0 for other values; [x] has its usual meaning as the number of positive integers ≦x.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 2 , December 1962 , pp. 139 - 142
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

(1) Carlitz, L., Some matrices related to the greatest integer function, Journal of the Elisha Mitchell Scientific Society, 76 (1960), 5–7.Google Scholar
(2) Cohen, Eckford, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, 74 (1960), 66–80.CrossRefGoogle Scholar
(3) Cohen, Eckford, Arithmetical notes, X. A class of totients, to appear in Proc. Anter. Math. Soc.Google Scholar
(4) Jacobsthal, E., Über die grösste ganze Zahl, II, Norske Videnskabers Selskab Forhandlinger (Trondheim), 30 (1957), 6–13Google Scholar