Jan 4 2024 - Untouchable Number Year

 

What is special about the number 2024? There are a lot of things if you are a mathematician.  I had no idea just how many things there are.   And I don't know the meaning of pretty well all of them.  We know what a prime number is, what a diver is, but a Cunningham number, a betrothed pair, a palindrome, and what about a polite number?  Aren't these all so curious and fascinating.   Here they are from Numbers Aplenty HERE: 2024 = 23 ⋅ 11 ⋅ 23   2024 has 16 divisors (see below), whose sum is σ = 4320. Its totient is φ = 880. The previous prime is 2017. The next prime is 2027. The reversal of 2024 is 4202. 2024 = T1 + T2 + ... + T22. 2024 = 23 + 33 + ... + 93. It is a Cunningham number, because it is equal to 452-1. 2024 is a nontrivial binomial coefficient, being equal to C(24, 3). Together with 2295 it forms a betrothed pair. It is a Harshad number since it is a multiple of its sum of digits (8). It is a plaindrome in base 9 and base 15. It is not an unprimeable number, because it can be changed into a prime (2027) by changing a digit. 2024 is an untouchable number, because it is not equal to the sum of proper divisors of any number. It is the 22-nd tetrahedral number. It is a pernicious number, because its binary representation contains a prime number (7) of ones. It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 77 + ... + 99. It is an arithmetic number, because the mean of its divisors is an integer number (270). 22024 is an apocalyptic number. It is an amenable number. It is a practical number, because each smaller number is the sum of distinct divisors of 2024, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2160). 2024 is an abundant number, since it is smaller than the sum of its proper divisors (2296). It is a pseudoperfect number, because it is the sum of a subset of its proper divisors. 2024 is a wasteful number, since it uses less digits than its factorization. 2024 is an odious number, because the sum of its binary digits is odd. The sum of its prime factors is 40 (or 36 counting only the distinct ones). The product of its (nonzero) digits is 16, while the sum is 8. The square root of 2024 is about 44.9888875168. The cubic root of 2024 is about 12.6494070868. Adding to 2024 its reverse (4202), we get a palindrome (6226). It can be divided in two parts, 202 and 4, that multiplied together give a palindrome (808). The spelling of 2024 in words is "two thousand, twenty-four", and thus it is an iban number. Divisors: 1 2 4 8 11 22 23 44 46 88 92 184 253 506 1012 2024

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