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The number 19 is not a harshad number in base 10, because the sum of the digits 1 and 9 is 10, and 19 is not divisible by 10. In base 10, every natural number expressible in the form 9R n a n , where the number R n consists of n copies of the single digit 1, n > 0, and a n is a positive integer less than 10 n and multiple of n , is a harshad ...
264 is an even composite number [1] with three distinct prime factors (2 3 × 3 × 11). [2] 264 is a Harshad number in base ten, [3] also divisible by each of its digits.264 is the sum of all even composite numbers that are not the sum of two abundant numbers (not necessarily distinct): 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 26 + 28 + 34 + 46. [4]
A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). A005349: Factorions: 1, 2, 145, 40585, ...
In base 10, the number 110 is a Harshad number [2] and a self number. [3] In other fields. 110 is also:
The sum of the base 10 digits of the integers 0, 1, 2, ... is given by OEIS: ... Harshad numbers are defined in terms of divisibility by their digit sums, ...
It is false that all highly composite numbers are also Harshad numbers in base 10. The first highly composite number that is not a Harshad number is 245,044,800; it has a digit sum of 27, which does not divide evenly into 245,044,800. 10 of the first 38 highly composite numbers are superior highly composite numbers.
[a] Furthermore, it is the first in the family of absolute Euler pseudoprimes, a subset of Carmichael numbers. [7] 1729 is divisible by 19, the sum of its digits, making it a harshad number in base 10. [8] 1729 is the dimension of the Fourier transform on which the fastest known algorithm for multiplying two numbers is based. [9]
102 is the first three-digit base 10 polydivisible number, since 1 is divisible by 1, 10 is divisible by 2 and 102 is divisible by 3. This also shows that 102 is a Harshad number. 102 is the first 3-digit number divisible by the numbers 3, 6, 17, 34 and 51. 102 64 + 1 is a prime number. There are 102 vertices in the Biggs–Smith graph.