Romer C. Castillo ¹

Affiliations
1 College of Accountancy, Business, Economics and International Hospitality Management, Batangas State University, Batangas City – 4200, PH

Abstract

Objectives: The paper aims to present a survey of both time-honored and contemporary studies on triangular number, factorial, relationship between the two, and some other numbers associated with them. Methods: The research is expository in nature. It focuses on expositions regarding the triangular number, its multiplicative analog – the factorial and other numbers related to them. Findings: Much had been studied about triangular numbers, factorials and other numbers involving sums of triangular numbers or sums of factorials. However, it seems that nobody had explored the properties of the sums of corresponding factorials and triangular numbers. Hence, explorations on these integers, called factoriangular numbers, were conducted. Series of experimental mathematics resulted to the characterization of factoriangular numbers as to its parity, compositeness, number and sum of positive divisors and other minor characteristics. It was also found that every factoriangular number has a runsum representation of length k, the first term of which is (k −1)! + 1 and the last term is (k −1)! + k . The sequence of factoriangular numbers is a recurring sequence and it has a rational closed-form of exponential generating function. These numbers were also characterized as to when a factoriangular number can be expressed as a sum of two triangular numbers and/or as a sum of two squares. Application/ Improvement: The introduction of factoriangular number and expositions on this type of number is a novel contribution to the theory of numbers. Surveys, expositions and explorations on existing studies may continue to be a major undertaking in number theory.

Keywords

Factorial, Factorial-like number, Factoriangular number, Polygonal number, Triangular number.

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Romer C. Castillo ¹

Affiliations
1 College of Accountancy, Business, Economics and International Hospitality Management, Batangas State University, Batangas City - 4200, PH

Abstract

Objectives: To analyze the six-year performance trend of a Philippine state university in the Customs Broker Licensure Examination and compare this performance with those of other schools. Methods: It is a quantitative research; statistical tables and graphs were used in data presentation and analysis. Data were mined from the database of the government agency in-charge of professional examinations. The schools considered for comparison are the top ten performing customs administration schools in the Philippines for the period 2011-2016; six of which, including the subject school, are from South Luzon and Metro Manila and four are from other regions. Findings: The subject university’s performance in the Customs Broker Licensure Examination for the period 2011-2016 is considered very satisfactory with its annual passing percentage way above the national passing percentage by 50% to 160% higher. Said university is the best-performing customs administration school in its region and second overall in the country in terms of licensure examination performance in the past six years. However, the subject school has decreasing passing percentage and the difference between this and the national average is also decreasing. Its competitor schools in the region and nearby region had been performing better and catching up with its performance in the last two years. The gap between the passing percentage of the subject school and the country’s leading customs administration school increased while its margin over the other top performing schools decreased in the last year. Applications/Improvements: It is, therefore, necessary that the subject university should design strategic measures to further enhance its performances to hold the lead in the region and be the best-performing customs school in the Philippines.

Keywords

Customs Administration, Customs Broker, Licensure Examination, Performance Trend

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