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In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. [1] [2] It is denoted by π(x) (unrelated to the number π). A symmetric variant seen sometimes is π 0 (x), which is equal to π(x) − 1 ⁄ 2 if x is exactly a prime number, and equal to π(x) otherwise.
The index is calculated from the results of a complete blood count. If the quotient of the mean corpuscular volume (MCV, in fL) divided by the red blood cell count (RBC, in million per microliter) is less than 13, β-thalassemia trait is said to be more likely. If the result is greater than 13, then iron-deficiency anemia is said to be more likely.
The first such distribution found is π(N) ~ N / log(N) , where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N).
For p an odd prime, count all digits greater than (p + 1) / 2; also count digits equal to (p + 1) / 2 unless final; and count digits equal to (p − 1) / 2 if not final and the next digit is counted. [2] The only known odd Catalan numbers that do not have last digit 5 are C 0 = 1, C 1 = 1, C 7 = 429, C 31, C 127 and C 255.
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
A Fermat number cannot be a perfect number or part of a pair of amicable numbers. The series of reciprocals of all prime divisors of Fermat numbers is convergent. (Křížek, Luca & Somer 2002) If n n + 1 is prime, there exists an integer m such that n = 2 2 m. The equation n n + 1 = F (2 m +m) holds in that case. [13] [14]
The simplest method for correcting the reticulocyte count, to obtain a more accurate daily production index, is to divide the corrected count by a factor of 2 (or multiply with ½) whenever polychromasia (the presence of immature marrow reticulocytes or "shift" cells) is observed on the smear or the immature fraction on the automated counter is ...
In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model. A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations. This necessitates an assessment of the fit of the chosen model.