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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.23 No.3

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Algebraic entropies of natural numbers with one or two prime factors

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.3, pp.205-221
https://doi.org/10.7468/jksmeb.2016.23.3.205
JEONG, SEUNGPIL
KIM, KYONG HOON
KIM, GWANGIL
JEONG,, S. , KIM,, K. H. , & KIM,, G. (2016). Algebraic entropies of natural numbers with one or two prime factors. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(3), 205-221, https://doi.org/10.7468/jksmeb.2016.23.3.205

Abstract

We formulate the additive entropy of a natural number in terms of the additive partition function, and show that its multiplicative entropy is directly related to the multiplicative partition function. We give a practical formula for the multiplicative entropy of natural numbers with two prime factors. We use this formula to analyze the comparative density of additive and multiplicative entropy, prove that this density converges to zero as the number tends to infinity, and empirically observe this asymptotic behavior.

keywords
entropy, partition function, additive entropy, multiplicative entropy, relative comparison density

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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