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Highly Powerful Number
In elementary number theory, a highly powerful number is a positive integer that satisfies a property introduced by the Indo-Canadian mathematician Mathukumalli V. Subbarao. The set of highly powerful numbers is a proper subset of the set of powerful number A powerful number is a positive integer ''m'' such that for every prime number ''p'' dividing ''m'', ''p''2 also divides ''m''. Equivalently, a powerful number is the product of a square and a cube, that is, a number ''m'' of the form ''m'' = ''a ...s. Define prodex(1) = 1. Let n be a positive integer, such that n = \prod_^k p_i^ , where p_1, \ldots , p_k are k distinct primes in increasing order and e_(n) is a positive integer for i = 1, \ldots ,k. Define \operatorname(n) = \prod_^k e_(n). The positive integer n is defined to be a highly powerful number if and only if, for every positive integer m,\, 1 \le m < n implies that The first 25 highly powerful nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathukumalli V
Mathukumalli is a village in Savalyapuram mandal of Guntur district in Andhra Pradesh Andhra Pradesh (, abbr. AP) is a state in the south-eastern coastal region of India. It is the seventh-largest state by area covering an area of and tenth-most populous state with 49,386,799 inhabitants. It is bordered by Telangana to the ..., India. Villages in Guntur district {{Guntur-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Powerful Number
A powerful number is a positive integer ''m'' such that for every prime number ''p'' dividing ''m'', ''p''2 also divides ''m''. Equivalently, a powerful number is the product of a square and a cube, that is, a number ''m'' of the form ''m'' = ''a''2''b''3, where ''a'' and ''b'' are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers ''powerful''. The following is a list of all powerful numbers between 1 and 1000: :1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576, 625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1000, ... . Equivalence of the two definitions If ''m'' = ''a''2''b''3, then every prime in the prime factorization of ''a'' appears in the prime factorization of ''m'' with an exponent of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
