An identity for a class of arithmetical functions of two variables

J. Chidambaraswamy and P. V. Krishnaiah

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-4

Abstract:

For a positive integer r , let r ∗ denote the quotient of r by its largest squarefree divisor ( 1 ∗ = 1 ) . Recently, K. R. Johnson proved that ( ∗ ) ∑ d | n | C ( d , r ) | = r ∗ ∏ p a ‖ n r ∗ p + r ( a + 1 ) ∏ p a ‖ n r ∗ p | r ( a ( p − 1 ) + 1 ) or 0 according as r ∗ | n or not where C ( n , r ) is the well known Ramanujan's sum. In this paper, using a different method, we generalize ( ∗ ) to a wide class of arithmetical functions of 2 variables and deduce as special cases ( ∗ ) and similar formulae for several generalizations of Ramanujan''s sum.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:180307

DOI: 10.1155/S0161171288000419

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