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The result must be divisible by 12. 324: 32 × 2 − 4 = 60 = 5 × 12. 13: Form the alternating sum of blocks of three from right to left. The result must be divisible by 13. [7] 2,911,272: 272 − 911 + 2 = −637. Add 4 times the last digit to the rest. The result must be divisible by 13. (Works because 39 is divisible by 13).
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
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.
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).
The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither ...
This method works fine for the year 2000 (because it is a leap year), and will not become a problem until 2100, when older legacy programs will likely have long since been replaced. Other programs contained incorrect leap year logic, assuming for instance that no year divisible by 100 could be a leap year.
The solar cycle is a 28-year cycle of the Julian calendar, and 400-year cycle of the Gregorian calendar with respect to the week.It occurs because leap years occur every 4 years, typically observed by adding a day to the month of February, making it February 29th.
These years are the only common years that are divisible by 4. In the obsolete Julian Calendar, all years that were divisible by 4 were leap years, meaning no century years could be common years. However, this rule adds too many leap days, resulting in the calendar drifting with respect to the seasons, which is the same thing that would happen ...