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36 depicted as a triangular number and as a square number 36 as the sum of the first positive cubes. 36 is both the square of six, and the eighth triangular number [1] or the sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number. [2]
a perfect number equals the sum of its proper divisors; that is, s(n) = ... 2, 11, 22 4 36 14 deficient, composite 23: 1, 23 2 24 1 deficient, prime 24:
Highly composite numbers: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... A positive integer with more divisors than any smaller positive integer. A002182: Superior highly composite numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A positive integer n for which there is an e > 0 such that d(n) / n e ≥ d(k) / k e for ...
Pursuing this type of analysis more carefully, G. H. Hardy and John Edensor Littlewood in 1923 conjectured (as part of their Hardy–Littlewood prime tuple conjecture) that for any fixed c ≥ 2, the number of representations of a large integer n as the sum of c primes n = p 1 + ⋯ + p c with p 1 ≤ ⋯ ≤ p c should be asymptotically equal to
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. [1] For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
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A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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