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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
40,832: 2 × 3 + 2 = 8, which is divisible by 4. 5: The last digit is 0 or 5. [2] [3] 495: the last digit is 5. 6: It is divisible by 2 and by 3. [6] 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6. Sum the ones digit, 4 times the 10s digit, 4 times the 100s digit, 4 times the ...
That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to 7 (which 420 is).
In the past 500 years, there was no leap day in 1700, 1800 and 1900, but 2000 had one. In the next 500 years, if the practice is followed, there will be no leap day in 2100, 2200, 2300 and 2500 ...
Thus, 1/54, in sexagesimal, is 1/60 + 6/60 2 + 40/60 3, also denoted 1:6:40 as Babylonian notational conventions did not specify the power of the starting digit. Conversely 1/4000 = 54/60 3 , so division by 1:6:40 = 4000 can be accomplished by instead multiplying by 54 and shifting three sexagesimal places.
There is a leap year in every year whose number is divisible by 4, but not if the year number is divisible by 100, unless it is also divisible by 400. So although the year 2000 was a leap year, the years 1700, 1800, and 1900 were common years.
Not all e i ≡ 2 (mod 5). [41] If all e i ≡ 1 (mod 3) or 2 (mod 5), then the smallest prime factor of N must lie between 10 8 and 10 1000. [41] More generally, if all 2e i +1 have a prime factor in a given finite set S, then the smallest prime factor of N must be smaller than an effectively computable constant depending only on S. [41]
360,360 = harmonic divisor number; [8] smallest number divisible by the numbers from 1 to 15 (there is no smaller number divisible by the numbers from 1 to 14 since any number divisible by 3 and 5 must be divisible by 15) 362,880 = 9!, highly totient number [5] 369,119 = prime number which divides the sum of all primes less than or equal to it [47]