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Some Generalizations of an Identity of Subhankulov
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- Journal:
- Canadian Mathematical Bulletin / Volume 20 / Issue 4 / 01 December 1977
- Published online by Cambridge University Press:
- 20 November 2018, pp. 489-494
- Print publication:
- 01 December 1977
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- Article
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In 1957, M. A. Subhankulov established the following identity
where
; μ is the Môbius function and J2 is the Jordan totient function of order 2. Since the Ramanujan trigonometrical sum C(nr) = ∑d| (n, r)dμ(r/d), we rewrite the above identity using C(n, r).In this paper, we give a generalization of Ramanujan's sum, which generalizes some of the earlier generalizations mainly due to E. Cohen, and prove a theorem from which we deduce some generalizations of the above identity.
; μ is the Môbius function and 