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An abundant number is a natural number n for which the sum of divisors σ(n) satisfies σ(n) > 2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n) satisfies s(n) > n. The abundance of a natural number is the integer σ(n) − 2n (equivalently, s(n) − n).
Centered square numbers, highlighted in red, are in found in the center of the odd rows, and are the sum of successive squares – taking 25 as an example, it is the sum of 16 (rotated yellow square) and the next smaller square, 9 (sum of blue triangles) The numbers along the left edge of the triangle are the lazy caterer's sequence and the ...
The following modification of the program is also used sometimes: Start: read // read n -> acc jmpz Done // jump to Done if nacc is 0. add sum // add sum to the acc store sum // store the new sum jump Start // go back & read in next number Done: load sum // load the final sum write // write the final sum stop // stop sum: .data 2 0 // 2-byte ...
A semiperfect number is a natural number that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers.
Sum of Natural Numbers (second proof and extra footage) includes demonstration of Euler's method. What do we get if we sum all the natural numbers? response to comments about video by Tony Padilla; Related article from New York Times; Why –1/12 is a gold nugget follow-up Numberphile video with Edward Frenkel
The natural numbers (positive integers) n ∈ . A000027: Triangular numbers t(n) ... A natural number that equals the sum of the factorials of its decimal digits.
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same abundancy form a friendly n-tuple.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.