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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.
As an example, 108 is a powerful number. Its prime factorization is 2 2 · 3 3, and thus its prime factors are 2 and 3.Both 2 2 = 4 and 3 2 = 9 are divisors of 108. However, 108 cannot be represented as m k, where m and k are positive integers greater than 1, so 108 is an Achilles number.
Number of ways to write an even number n as the sum of two primes (sequence A002375 in the OEIS) A very crude version of the heuristic probabilistic argument (for the strong form of the Goldbach conjecture) is as follows. The prime number theorem asserts that an integer m selected at random has roughly a โ 1 / ln m โ chance of being prime.
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
Number bonds are often learned in sets for which the sum is a common round number such as 10 or 20. Having acquired some familiar number bonds, children should also soon learn how to use them to develop strategies to complete more complicated sums, for example by navigating from a new sum to an adjacent number bond they know, i.e. 5 + 2 and 4 ...
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