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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
144, or twice 72, is also highly totient, as is 576, the square of 24. [8] While 17 different integers have a totient value of 72, the sum of Euler's totient function φ(x) over the first 15 integers is 72. [9] It also is a perfect indexed Harshad number in decimal (twenty-eighth), as it is divisible by the sum of its digits . [10]
For instance, to find the product of 13 and 21 one had to double 21 three times, obtaining 2 × 21 = 42, 4 × 21 = 2 × 42 = 84, 8 × 21 = 2 × 84 = 168. The full product could then be found by adding the appropriate terms found in the doubling sequence: [ 16 ]
The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. It was popularized in Kasner's 1940 book Mathematics and the Imagination, where it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 10 10 100), was also introduced in that book.
9 is the sum of the cubes of the first two non-zero positive integers + which makes it the first cube-sum number greater than one. [6] It is also the sum of the first three nonzero factorials! +! +!, and equal to the third exponential factorial, since =. [7]
Today's NYT Connections puzzle for Friday, December 13, 2024The New York Times
Using the same argument as before it becomes clear that the number on the gate is 13, and the ages 9, 2 and 2. [ 5 ] A criticism of this problem is that a household may have two children of the same age in terms of natural numbers, but different birthdays, such as children in a mixed-parent household.
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