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A square has even multiplicity for all prime factors (it is of the form a 2 for some a). The first: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (sequence A000290 in the OEIS). A cube has all multiplicities divisible by 3 (it is of the form a 3 for some a). The first: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 (sequence A000578 ...
Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld. Selected prime related sequences in OEIS. Fischer, R. Thema: Fermatquotient B^(P−1) == 1 (mod P^2) (in German) (Lists Wieferich primes in all bases up to 1052) Padilla, Tony (7 February 2013).
The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p. The largest 18 of these have been discovered by the distributed computing project Great Internet Mersenne Prime Search , or GIMPS; their discoverers are listed as "GIMPS / name ", where the name ...
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 powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m.Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers.
Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3.
This article lists the 250 largest city squares in the world in descending order of area. The areas given are as noted in the articles and references provided, but may not be directly comparable. The areas given are as noted in the articles and references provided, but may not be directly comparable.
which is both the t-th triangular number and the s-th square number. A near-isosceles Pythagorean triple is an integer solution to a 2 + b 2 = c 2 where a + 1 = b. The next table shows that splitting the odd number H n into nearly equal halves gives a square triangular number when n is even and a near isosceles Pythagorean triple when n is odd ...