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A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number , other examples being square numbers and cube numbers . The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...
5041 = 71 2, centered octagonal number [2] 5050 – triangular number, Kaprekar number, [3] sum of first 100 integers; 5051 – Sophie Germain prime; 5059 – super-prime; 5076 – decagonal number [4] 5077 – prime of the form 2p-1; 5081 – Sophie Germain prime; 5087 – safe prime; 5099 – safe prime
Square triangular number 36 depicted as a triangular number and as a square number. In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number. There are infinitely many square triangular numbers; the first few are:
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
The number of domino tilings of a 4×4 checkerboard is 36. [10] Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number. [11] The sum of the integers from 1 to 36 is 666 (see number of the beast). 36 is also a ...
120 is . the factorial of 5, i.e., ! =.; the fifteenth triangular number, [2] as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is the smallest number to appear six times in Pascal's triangle (as all triangular and tetragonal numbers appear in it).
It is the first member of the first cluster of three semiprimes 33, 34, 35; the next such cluster is 85, 86, 87. [9] It is also the smallest integer such that it and the next two integers all have the same number of divisors (four). [10] 33 is the number of unlabeled planar simple graphs with five nodes. [11]