A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other...

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...

mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words, the...

16 Egyptian fraction 1012 = ternary number, (3210) quadruple triangular number (triangular number is 253), number of partitions of 1 into reciprocals...

non-trivial square triangular number. Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than...

properties of oblong, triangular, and square numbers: 1 . The number 10 for example, can be arranged as a triangle (see triangular number): But 10 cannot be...

003 = Smallest 7-digit prime number 1,000,405 = Smallest triangular number with 7 digits and the 1,414th triangular number 1,002,001 = 10012, palindromic...

666 is the largest triangular number that is also a repdigit. Since 36 is a triangular number too, 666 is a doubly triangular number. 666 is the sum of...

A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns...

19. 19 is the third centered triangular number as well as the third centered hexagonal number. The 19th triangular number is 190, equivalently the sum...

406 = 2 × 7 × 29, sphenic number, 28th triangular number, centered nonagonal number, even nontotient, Narayana's cow number HTTP status code for "Not...

constant 6181 – octahedral number 6200 – harmonic divisor number 6201 – square pyramidal number 6216 – triangular number 6217 – super-prime, prime of...

n} th triangular number, then the doubly triangular numbers are the numbers of the form T T n {\displaystyle T_{T_{n}}} . The doubly triangular numbers...

is prime 2015 – Lucas–Carmichael number 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 211-25 2017 – Mertens function zero...

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

divides the Euclid number 2999# + 1 3003 – triangular number, only number known to appear eight times in Pascal's triangle; no number is known to appear...

= 7!, superior highly composite number 5041 = 712, centered octagonal number 5050 – triangular number, Kaprekar number, sum of first 100 integers 5051...

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...

605 = 5 × 112, Harshad number, sum of the nontriangular numbers between the two successive triangular numbers 55 and 66, number of non-isomorphic set-systems...

centered triangular number, happy number 902 = 2 × 11 × 41, sphenic number, nontotient, Harshad number 903 = 3 × 7 × 43, sphenic number, 42nd triangular number...

cube numbers and triangular numbers). In the real number system, square numbers are non-negative. A non-negative integer is a square number when its square...

the eleventh nontotient (with 50 the fifth). The twelfth triangular number 78 is the only number to have an aliquot sum equal to 90, aside from the square...

this approximation end in 6 and generate a sum of 28 (the seventh triangular number), numbers which represent the first and second perfect numbers, respectively...

number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number,...

+ 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number, sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231) 803 = 11 × 73, sum of three...

pronic number, nontotient, Harshad number 703 = 19 × 37, the 37th triangular number, a hexagonal number, smallest number requiring 73 fifth powers for Waring...

triangle (as all triangular and tetragonal numbers appear in it). Because 15 is also triangular, 120 is a doubly triangular number. 120 is divisible...

003 = smallest 6-digit prime number 100,128 = smallest triangular number with 6 digits and the 447th triangular number 100,151 = twin prime with 100...

2^{p-1}(2^{p}-1)} , each even perfect number is the ( 2 p − 1 ) {\displaystyle (2^{p}-1)} -th triangular number (and hence equal to the sum of the integers...