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The sum of the ones digit, double the tens digit, and four times the hundreds digit is divisible by 8. 34,152: 4 × 1 + 5 × 2 + 2 = 16. 9: The sum of the digits must be divisible by 9. [2] [4] [5] 2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9. Subtracting 8 times the last digit from the rest gives a multiple of 9. (Works because 81 is divisible by 9)
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
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 ...
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. 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 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 number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).
Year 100 was a leap year starting on Wednesday of the Julian calendar. The denomination 100 for this year has been used since the early medieval period.