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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Perfect Number, Mersenne Prime, 6, 28, List of Perfect Numbers, 496, 8128. Excerpt:27 29 28 28 ( twenty-eight ) is the natural number following 27 and preceding 29. In mathematics It is a composite number , its proper divisors being 1 , 2 , 4 , 7 , and 14. Twenty-eight is the second perfect number . As a perfect number, it is related to the Mersenne prime 7, since 2 (2 - 1) = 28. The next perfect number is 496, the previous being 6 . Twenty-eight is the sum of the totient function for the first nine integers. Twenty-eight is not the aliquot sum of any number other than itself and is therefore not a component in an aliquot sequence . Since the greatest prime factor of 28 + 1 = 785 is 157, which is more than 28 twice, 28 is a Størmer number . Twenty-eight is a harmonic divisor number , a happy number , a triangular number , a hexagonal number ,and a centered nonagonal number . It appears in the Padovan sequence , preceded by the terms 12, 16, 21 (it is the sum of the first two of these). It is also a Keith number , because it recurs in a Fibonacci -like sequence started from its base 10 digits: 2, 8, 10, 18, 28... Twenty-eight is the third positive integer with a prime factorization of the form 2 q where q is an odd prime . Twenty-eight is the ninth and last number in early Indian magic square of order 3. There are twenty-eight convex uniform honeycombs . Twenty-eight is the only positive integer that has a unique Kayles nim-value . In science Astronomy In other fields Twenty-eight is: item An abbreviation for such years as 1928 and 2028. item In Gematriya , the system of Hebrew Numerolo... ... Read more

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Chapters: Prime Number, Factorial, Binomial Coefficient, Perfect Number, Carmichael Number, Integer Sequence, Mersenne Prime, Bernoulli Number, Euler Number, Fermat Number, Square-Free Integer, Amicable Number, Stirling Number, Partition, Lah Number, Super-Poulet Number, Arithmetic Progression, Derangement, Composite Number, On-Line Encyclopedia of Integer Sequences, Pell Number, Catalan Number, Power of Two, Sylvester's Sequence, Regular Number, Polite Number, Ménage Problem, Greedy Algorithm for Egyptian Fractions, Hofstadter Sequence, Elliptic Divisibility Sequence, Powerful Number, Znám's Problem, Bell Number, Singly and Doubly Even, Hyperperfect Number, Strict Weak Ordering, Calkin-wilf Tree, Beatty Sequence, Practical Number, Padovan Sequence, Highly Composite Number, Triangular Number, King Wen Sequence, Eulerian Number, Square Triangular Number, Figurate Number, Lucas Sequence, Squared Triangular Number, Perrin Number, Multiplicative Partition, Cube, Smooth Number, Primorial, Lambek-moser Theorem, Meander, Primefree Sequence, Small Set, Harmonic Divisor Number, Friendly Number, Lazy Caterer's Sequence, Semiprime, Abundant Number, Perfect Totient Number, Juggler Sequence, Antichain, Perfect Power, Lucas Number, Cullen Number, Double Mersenne Number, Superabundant Number, Strictly Non-Palindromic Number, Boustrophedon Transform, Somos Sequence, Woodall Number, Lucky Number, Highly Abundant Number, Leyland Number, Factorion, Primary Pseudoperfect Number, Ban Number, Weird Number, Jacobsthal Number, Sociable Number, Almost Prime, Superperfect Number, Motzkin Number, Pronic Number, Ulam Numbers, Carol Number, Refactorable Number, Idoneal Number, Euclid-mullin Sequence, Deficient Number, Thabit Number, Alternating Factorial, Primorial Prime, Achilles Number, Semiperfect Number, Fractal Sequence, Untouchable Number, Erdős-woods Number, Multiply Perfect Number, Sphenic Number, Blum Integer, Zeisel Number, Giuga Number, Nontoti...More: http://booksllc.net/?id=4964 ... Read more

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Based on lectures given by Professor Hlawka in Vienna and in Pasadena, the book covers diophantine approximation, uniform distribution of numbers modulo 1 and geometry of numbers, as well as analytic number theory. It also proves the irrationality of zeta (3) and presents the important method of A. and H. Lenstra for the decomposition of polynomials, neither available in any other textbook. Various proofs of the prime number theorem are described. This monograph on number theory, real analysis, algebra/algebraic number theory is intended for students and lecturers in the above fields. ... Read more