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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 ...
2012 – The number 8 × 10 2012 − 1 is a prime number [10] 2013 – number of widely totally strongly normal compositions of 17; 2014 – 5 × 2 2014 - 1 is prime [11] 2015 – Lucas–Carmichael number [12] 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, [13] 2 11-2 5; 2017 – Mertens function zero, sexy ...
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
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 ...
The first: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 (sequence A005843 in the OEIS). An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a).
1007 = number that is the sum of 8 positive 5th powers [9] 1008 = divisible by the number of primes below it; 1009 = smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (838 11, 474 15, 2F2 19, 1I1 24, 181 28). It is also a Lucky prime and Chen prime. 1010 = 10 3 + 10, [10] Mertens function zero
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, s(a)=b and s(b)=a, where s(n)=σ(n)-n is equal to the sum of positive divisors of n except n itself (see also divisor function). The smallest pair of amicable numbers is ...
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.