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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]
All square triangular numbers have the form , where is a convergent to the continued fraction expansion of , the square root of 2. [ 4 ] A. V. Sylwester gave a short proof that there are infinitely many square triangular numbers: If the n {\displaystyle n} th triangular number n ( n + 1 ) 2 {\displaystyle {\tfrac {n(n+1)}{2}}} is square, then ...
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.
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 ...
Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous ...
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Ramanujan's constant [36] 262 53741 26407 68743 .99999 99999 99250 073 ... Rational numbers have two continued fractions; the version in this list is the shorter one.
A number n that has more divisors than any x < n is a highly composite number (though the first two such numbers are 1 and 2). Composite numbers have also been called "rectangular numbers", but that name can also refer to the pronic numbers, numbers that are the product of two consecutive integers. Yet another way to classify composite numbers ...