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238: 23 × 3 + 8 × 2 = 85. 18: It is divisible by 2 and by 9. [6] 342: it is divisible by 2 and by 9. 19: Add twice the last digit to the rest. (Works because (10a + b) × 2 − 19a = a + 2b; since 19 is a prime and 2 is coprime with 19, a + 2b is divisible by 19 if and only if 10a + b is.) 437: 43 + 7 × 2 = 57. Add 4 times the last two ...
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 digit sum of 2946, for example is 2 + 9 + 4 + 6 = 21. Since 21 = 2946 − 325 × 9, the effect of taking the digit sum of 2946 is to "cast out" 325 lots of 9 from it. If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12.
(86·10 n + 31) / 9 or 95 + 9 (89·10 n + 593) / 9 or 98 + 23; In each case, every term is divisible by one of the primes from the set {3, 7, 11, 13}. [8] These primes can be said to form a covering set exactly analogous to Sierpinski and Riesel numbers. [9] The covering set {3, 7, 11, 37} is found for several similar sequences, [9] including:
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).
Klay Thompson scored 25 points, Daniel Gafford gave the Mavericks 15 rebounds in what could be his last start at center for a while and Dallas beat the Boston Celtics 127-120 on Thursday night in ...
In mathematics, a square-free integer (or squarefree integer) is an integer which is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 3 2. The smallest ...
(The Center Square) - An Illinois-based Black health advocacy group is demanding more tax dollars for Black HIV care. Officials from the group Black Leadership Advocacy Coalition for Healthcare ...