Cohen, Eckford Arithmetical functions associated with the unitary divisors of an integer. (English) Zbl 0094.02601 Math. Z. 74, 66-80 (1960). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 ReviewsCited in 43 Documents Keywords:number theory PDFBibTeX XMLCite \textit{E. Cohen}, Math. Z. 74, 66--80 (1960; Zbl 0094.02601) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Unitary totient (or unitary phi) function uphi(n). Decimal expansion of Product_{p prime} (1 - 1/(p*(p+1))). Decimal expansion of Product_{p prime} (1 - 1/(p^2*(p+1))). a(n) = mu(rad(n)), where mu is the Moebius-function (A008683) and rad is the radical or squarefree kernel (A007947). Sum of unitary, squarefree divisors of n, including 1. Partial sums of A047994. Exponentially odd numbers. The number of exponentially odd numbers <= 10^n. Table read by downward antidiagonals: T(n,k) is the greatest divisor of n which is a unitary divisor of k. Partial sums of A092261. Decimal expansion of Pi^2/(12*zeta(3)). References: [1] Cohen, E.: An extension ofRamanujan’s sum, III. Connections with totient functions. Duke Math. J.23, 623-630 (1956). · Zbl 0073.02902 [2] Cohen, E.: Trigonometric sums in elementary number theory. Amer. Math. Monthly66, 105-117 (1959). · Zbl 0084.27001 [3] Dickson, L. E.: History of the Theory of Numbers, vol. I. New York, reprinted 1952. · JFM 48.0137.02 [4] Dirichlet, P. G. Lejeune: Vorlesungen über Zahlentheorie, 4th ed. Brunswick 1894 (edited byR. Dedekind). [5] Fekete, M.: Über die additive Darstellung einiger zahlentheoretischer Funktionen. Math. u. naturwiss. Berichte aus Ungarn26, 196-211 (1913). · JFM 44.0209.01 [6] Hardy, G. H., andE. M. Wright: Introduction to the Theory of Numbers, 3rd ed. Oxford 1954. · Zbl 0058.03301 [7] Lerch, M.: Démonstration élémentaire d’un théorème d’arithmétique. Sitzungsber. der Böhmischen Ges. Wiss., Prag, No. 2, 1903, 3pp. [8] Vaidyanathaswamy, R.: The theory of multiplicative arithmetical functions. Trans. Amer. Math. Soc.33, 579-662 (1931). · Zbl 0002.12402 [9] Wigert, S.: Sur quelques formules asymptotiques de la théorie des nombres. Arkiv för Mat. Astr. Fys.22, 6 pp. (1932). · JFM 58.0189.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.