# RECURRENCE RELATION IN NUMBER THEORY

• Mannu Arya et. al

### Abstract

The research is on recurrence relation in

The research is on recurrence relation in number theory, with the sole aim of reviewing subtle and far-ending relationships in selected natural numbers which includes the composite and perfect numbers. Related literature was reviewed on which serves as the basis for critical analysis of the natural numbers. From the findings, it was found that there is a degree of relationship between prime numbers and perfect numbers including composite numbers. The nth composite number () can be generated using the Wolfram Language code. This is a machine code. It is very difficult to establish a manual formula to extrapolate far composite numbers, but Dirichlet generating function is used to establish the characteristic function of the composite numbers.  Furthermore, the relation in perfect numbers can be addressed thus as follows; (Power of Two) × (Double that Power - 1). The prime number formula is given by. To get the Perfect Number, the formula becomes (. Getting the nth sequence of a perfect number is dependent on the equivalent nth sequence of prime numbers. The research finally concludes with the call for researchers to team up to make more explicit, the recurrence relation in composite numbers.

number theory, with the sole aim of reviewing subtle and far-ending relationships in selected natural numbers which includes the composite and perfect numbers. Related literature was reviewed on which serves as the basis for critical analysis of the natural numbers. From the findings, it was found that there is a degree of relationship between prime numbers and perfect numbers including composite numbers. The nth composite number () can be generated using the Wolfram Language code. This is a machine code. It is very difficult to establish a manual formula to extrapolate far composite numbers, but Dirichlet generating function is used to establish the characteristic function of the composite numbers.  Furthermore, the relation in perfect numbers can be addressed thus as follows; (Power of Two) × (Double that Power - 1). The prime number formula is given by. To get the Perfect Number, the formula becomes (. Getting the nth sequence of a perfect number is dependent on the equivalent nth sequence of prime numbers. The research finally concludes with the call for researchers to team up to make more explicit, the recurrence relation in composite numbers.

Published
2020-01-13
How to Cite
et. al, M. A. (2020). RECURRENCE RELATION IN NUMBER THEORY. International Journal of Advanced Science and Technology, 29(2), 885 - 893. Retrieved from http://sersc.org/journals/index.php/IJAST/article/view/3269
Section
Articles