Ivars Peterson's MathTrek - Cubes of Perfection
Ivars Peterson's MathTrek May 18, 1998 Cubes of Perfection Playing with integers can lead to all sorts of little surprises. A whole number that is equal to the sum of all its possible divisors --including 1 but not the number itself -- is known as a perfect number (see A Perfect Collaboration). For example, the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 equals 6. Six is the smallest ...
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On a Generalization of Perfect Numbers
On a Generalization of Perfect Numbers A Problem Proposal ABSTRACT. This paper presents a notion of perfect numbers relative to arithmetical functions: an arithmetical function f produces a set of f-perfect numbers. Two among the many examples considered are small perturbations of the normal definition; late in these two sequences, odd perfect numbers appear! (Could the situation be similar for ...
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Perfect numbers
Perfect numbers Number theory index History Topics Index It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. It is quite likely, although not certain, that the Egyptians would have come across such numbers naturally given the way their methods of calculation worked, see for example where ...
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