Silver ratioIn mathematics, two quantities are in the silver ratio (or silver mean) if the ratio of the smaller of those two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice the larger quantity (see below). This defines the silver ratio as an irrational mathematical constant, whose value of one plus the square root of 2 is approximately 2.4142135623.
Perrin numberIn mathematics, the Perrin numbers are defined by the recurrence relation P(n) = P(n − 2) + P(n − 3) for n > 2, with initial values P(0) = 3, P(1) = 0, P(2) = 2. The sequence of Perrin numbers starts with 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, ... The number of different maximal independent sets in an n-vertex cycle graph is counted by the nth Perrin number for n > 1. This sequence was mentioned implicitly by Édouard Lucas (1876). In 1899, the same sequence was mentioned explicitly by François Olivier Raoul Perrin.
PrimorialIn mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers. The name "primorial", coined by Harvey Dubner, draws an analogy to primes similar to the way the name "factorial" relates to factors. For the nth prime number pn, the primorial pn# is defined as the product of the first n primes: where pk is the kth prime number.
72 (number)72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal). Seventy-two is a pronic number, as it is the product of 8 and 9. It is the smallest Achilles number, as it's a powerful number that is not itself a power. 72 is an abundant number. With exactly twelve positive divisors, including 12 (one of only two sublime numbers), 72 is also the twelfth member in the sequence of refactorable numbers.
Square root of 5The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as: It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are: 2.23606 79774 99789 69640 91736 68731 27623 54406 18359 61152 57242 7089.
40 (number)40 (forty) is the natural number following 39 and preceding 41. Though the word is related to four (4), the spelling forty replaced fourty during the 17th century and is now the standard form. Forty is the fourth octagonal number. As the sum of the first four pentagonal numbers: , it is also is the fourth pentagonal pyramidal number. Forty is a repdigit in ternary, and a Harshad number in decimal. 40 is the smallest number with exactly nine solutions to the equation Euler's totient function (for values 41, 55, 75, 82, 88, 100, 110, 132, and 150 of ).
25 (number)25 (twenty-five) is the natural number following 24 and preceding 26. It is a square number, being 52 = 5 × 5, and hence the third non-unitary square prime of the form p2. It is one of two two-digit numbers whose square and higher powers of the number also ends in the same last two digits, e.g., 252 = 625; the other is 76. Twenty five has an even aliquot sum of 6, which is itself the first even and perfect number root of an aliquot sequence; not ending in (1 and 0).
Superabundant numberIn mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant precisely when, for all m < n where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... . For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5.
16 (number)16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and . 16 is the first non-unitary fourth-power prime of the form p4 The aliquot sum of a 2-power (2n) is always one less than the 2-power itself therefore the aliquot sum of 16 is 15, within an aliquot sequence of four composite members (16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
48 (number)48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens. Forty-eight is the double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number. 48 is the smallest number with exactly ten divisors, and the first multiple of 12 not to be a sum of twin primes. The Sum of Odd Anti-Factors of 48 = number * (n/2) where n is an Odd number. So, 48 is an Odd Anti-Factor Hemiperfect Number.
