Analytical Representations of Divisors of Integers
Institute for the History of Science
Polish Academy of Sciences
E-mail: krzysiek2357@gmail.com
Received:
Received: 24 February 2017; accepted: 03 April 2017; published online: 13 April 2017
DOI: 10.12921/cmst.2017.0000014
Abstract:
Certain analytical expressions which ”feel“ the divisors of natural numbers are investigated. It is shown that these expressions encode to some extent the well-known algorithm of the sieve of Eratosthenes.
Key words:
factorization, number theory, one-variable calculus, primality
References:
[1] On-Line Encyclopedia of Integer Sequences, sequence number A054525.
[2] T.M. Apostol, Modular Forms and Dirichlet Series in Analysis, 1976, Springer-Verlag.
[3] D.N. Cox, Visualizing the Sieve of Eratosthenes, Notices of the AMS 55(5), 579-582 (2008).
[4] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, 1993, John Wiley and Sons.
[5] R.M. Redheffer, Eine explizit lösbare Optimierungsaufgabe, Internat. Schriftenreihe Numer. Math. vol. 36, 1977.
[6] M. Trott, The Mathematica GuideBook for Programming, 2004, New York: Springer-Verlag.
[7] J.J. Ventrella, Divisor Drips and Square Root Waves – Prime Numbers are the Holes in Complex Composite Number Patterns, 2010, Eyebrain Books (book web site: www.divisorplot.com).
Certain analytical expressions which ”feel“ the divisors of natural numbers are investigated. It is shown that these expressions encode to some extent the well-known algorithm of the sieve of Eratosthenes.
Key words:
factorization, number theory, one-variable calculus, primality
References:
[1] On-Line Encyclopedia of Integer Sequences, sequence number A054525.
[2] T.M. Apostol, Modular Forms and Dirichlet Series in Analysis, 1976, Springer-Verlag.
[3] D.N. Cox, Visualizing the Sieve of Eratosthenes, Notices of the AMS 55(5), 579-582 (2008).
[4] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, 1993, John Wiley and Sons.
[5] R.M. Redheffer, Eine explizit lösbare Optimierungsaufgabe, Internat. Schriftenreihe Numer. Math. vol. 36, 1977.
[6] M. Trott, The Mathematica GuideBook for Programming, 2004, New York: Springer-Verlag.
[7] J.J. Ventrella, Divisor Drips and Square Root Waves – Prime Numbers are the Holes in Complex Composite Number Patterns, 2010, Eyebrain Books (book web site: www.divisorplot.com).