Two arithmetic functions

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 4, 1998, Number 2, Pages 57–79
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A. G. Shannon
University of Technology, Sydney, 2007, Australia

References

1. Alter, Ronald (1973) Can </>(0) properly divide n – 1? Americal Mathematical Monthly. 80: 192-193.
2. Andrews, George E. (1971) Number Theory. Philadelphia: W.B. Saunders.
3. Carlitz, L. (1960) Some arithmetic sums connected with the greatest integer function. Mathematica Scandinavica. 8: 59-64.
4. Conway, John H. h Guy, Richard K. (1996) The Book of Numbers. New York: Copernicus Springer-Verlag.
5. Cunat Collado, Francisco (1980) Nota. Gaceta Mathematica. 32: 50-51.
6. Gomez Sanchez, Jesus (1979) Un teorema de la teorza analztica de numeros. Gaceta Mathematica. 31: 119-121.
7. Hardy, G.H. &; Wright, E.M. (1965) An Introduction to the Theory of Numbers. Fourth Edition. Oxford: Clarendon Press.
8. Horadam, A.F. & Shannon, A.G (1976) Ward’s Staudt-Clausen problem. Mathematica Scandinavica. 39: 239-250.
9. Horadam, E.M. (1961) Arithmetical functions of generalized primes. American Mathematical Monthly. 68: 626-629.
10. Horadam, E.M. (1962) Arithmetical functions associated with the unitary divisors of a generalized integer. American Mathematical Monthly. 69: 196-199.
11. Horadam, E.M. (1963a) Arithmetical functions of generalized integers. Ph.D. thesis, University of New England.
12. Horadam, E.M. (1963b) The Euler </> function for generalized integers. Proceedings of the American Mathematical Society. 14: 754-762.
13. Horadam, E.M. (1963c) A calculus of convolutions for generalized integers. Indagationes Mathematicae. 25: 695-698.
14. Horadam, E.M. (1964) Ramanujan’s sum for generalized integers. Duke Mathematical Journal. 31: 697-702.
15. Horadam, E.M. (1966a) Addendum to Ramanujan’s sum for generalized integers. Duke Mathematical Journal. 33: 705-707.
16. Horadam, E.M. (1966b) Exponential functions for arithmetical semigroups. Journal fur die Heine und Angewandte Mathematik. 222: 14-19.
17. Horadam, E.M. (1971) An extension of Daykin’s generalized Mobius function to unitary divisors. Journal fur die Heine und Angewandte Mathematik. 246: 117-125.
18. Iverson, Kenneth E, (1980) Notation as a tool of thought. Communications of the Association for Computing Machinary. 23: 444-464.
19. Jager, H. (1961) The unitary analogues of some identities for certain arithmetical functions. Knoninklijke Nederlandse Akademie van Wetenschappen Indagationes Mathemat- icae. 23: 508.
20. Popken, J. (1955) On convolutions in number theory. Knoninklijke Nederlandse Akademie van Wetenschappen Indagationes Mathematicae. 17: 10-15.
21. Ribenboim, Paulo (1997) Are there functions that generate prime numbers? College Mathematics Journal. 28: 352-359.
22. Shannon, A.G. (1974) Some properties of a fundamental recursive sequence of arbitrary order. The Fibonacci Quarterly. 12: 327-335.
23. Shannon, A.G. (1982) Dos funciones aritmeticas. Gaceta Mathematica. 34: 82-91.
24. Sita Rama Chandra Rao, R & Sita Ramaiah, V. (1979) Ramanujan sums in regular arithmetic convolutions (abstract). Mathematics Student. 45: 10-11.
25. Sloane, N.J.A. & Plouffe, Simon (1995) The Encyclopedia of Integer Sequences. San Diego: Academic Press.