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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
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 ).
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
Given a score of 22 — a singly even number — one has a game shot for double 11. If one hits single 11, the new score is 11, which is odd, and it will take at least two further darts to recover. By contrast, when shooting for double 12, one may make the same mistake but still have 3 game shots in a row: D12, D6, and D3.
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 ...
divisible by the value of its φ function, which is 36. divisible by the total number of its divisors (12), hence it is a refactorable number. the angle in degrees of the interior angles of a regular pentagon in Euclidean space. palindromic in bases 11 (99 11), 17 (66 17), 26 (44 26), 35 (33 35) and 53 (22 53)