Divisor Function, Leonidas Alaoglu, Paul Erdős, Riemann Hypothesis, Harshad Number, Superabundant Number
Phon
(2012-01-06
)
eligible for voucher
ISBN-13:
978-613-9-15531-6
ISBN-10:
6139155312
EAN:
9786139155316
Book language:
English
Blurb/Shorttext:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. Formally, a natural number n is called superabundant precisely when, for any m > n,frac{sigma(m)}{m} > frac{sigma(n)}{n} where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... (sequence A004394 in OEIS). Superabundant numbers were defined by Leonidas Alaoglu and Paul Erdős (1944). Unknown to Alaoglu and Erdos, about 30 pages of Ramanujan's 1915 paper "Highly Composite Numbers" were suppressed.