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.
JJ, or j, is the tenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its usual name in English is jay (pronounced 'dʒeɪ), with a now-uncommon variant jy 'dʒaɪ. When used in the International Phonetic Alphabet for the voiced palatal approximant, it may be called yod or jod (pronounced 'jɒd or 'joʊd). The letter J used to be used as the swash letter I, used for the letter I at the end of Roman numerals when following another I, as in XXIIJ or xxiij instead of XXIII or xxiii for the Roman numeral twenty-three.
60 (number)60 (sixty) () is the natural number following 59 and preceding 61. Being three times 20, it is called threescore in older literature (kopa in Slavic, Schock in Germanic). 60 is a highly composite number. Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect number. 60 is a Twin-prime sum of the fifth pair of twin-primes, 29 + 31.
Sparsely totient numberIn mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, where is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660, 9870, ... .
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.
120 (number)120 (one hundred [and] twenty) is the natural number following 119 and preceding 121. In the Germanic languages, the number 120 was also formerly known as "one hundred". This "hundred" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts. 120 is the factorial of 5, i.e., . the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number.
Perfect numberIn number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, where is the sum-of-divisors function.
Colossally abundant numberIn mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors. Particularly, it's defined by a ratio between the sum of an integer's divisors and that integer raised to a power higher than one. For any such exponent, whichever integer has the highest ratio is a colossally abundant number. It is a stronger restriction than that of a superabundant number, but not strictly stronger than that of an abundant number.
