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Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1×1 + 7×3 + 3×2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if ...
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
An abundant number whose abundance is greater than any lower number is called a highly abundant number, and one whose relative abundance (i.e. s(n)/n ) is greater than any lower number is called a superabundant number; Every integer greater than 20161 can be written as the sum of two abundant numbers. The largest even number that is not the sum ...
The digit sum of 2946, for example is 2 + 9 + 4 + 6 = 21. Since 21 = 2946 − 325 × 9, the effect of taking the digit sum of 2946 is to "cast out" 325 lots of 9 from it. If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12.
In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
1 2 5 (q, changes from 000 to 100 to 1 20 to 1 2 5 ... So 1 and 12 are less than 37, but 126 is greater. Next, the greatest multiple of 37 less than or equal to 126 ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]
For example, 6 is highly composite because d(6)=4 and d(n)=1,2,2,3,2 for n=1,2,3,4,5 respectively. A related concept is that of a largely composite number , a positive integer that has at least as many divisors as all smaller positive integers.