Analytical Representations of Divisors of Integers

• Autorzy: Maślanka K.

Identyfikatory

DOI

10.12921/cmst.2017.0000014

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

number theory; factorization; primality; one-variable calculus

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2017
• Tom: Vol. 23, No. 2
• Strony: 85--91
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Maślanka K.

• Institute for the History of Science Polish Academy of Sciences

Bibliografia

• [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).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).