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Multiply Abundant Numbers
Author(s) -
Miller Gordon L.,
Whalen Mary T.
Publication year - 1995
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/j.1949-8594.1995.tb15776.x
Subject(s) - combinatorics , mathematics , order (exchange) , number theory , arithmetic , real number , code (set theory) , discrete mathematics , computer science , finance , economics , set (abstract data type) , programming language
A multiply abundant number N of order r is a number for which the sum of the proper divisors, S(N), is greater than r times N. The authors explore abundant, double abundant, and triple abundant numbers as well as abundant numbers of higher orders. They also consider odd abundant numbers of orders greater than 1. They present a proof that abundant numbers of every order r exist. Readers are encouraged to use the included computer code to explore abundant numbers for themselves, look for patterns in the output, and consider further questions about these fascinating numbers.