Year 2016 had some interesting properties (apart those listed below):

•
2016 is the smallest natural number whose square root (44.89988864...) starts with 10 composite digits.

•
2016 is in smallest amicable triple (1980, 2016, 2556), i.e., a set of 3 numbers whose sum of divisors (6552) is equal the sum of the 3 numbers.

•
2016 is the only natural number *n* such that the sum *n*^{2} + *n*^{3} is stricty pandigital, i.e., it contains all the 10 digits exactly once. Indeed, 2016^{2} + 2016^{3} =
8197604352.

•
2016 = 2^{11} - 2^{5} =
3^{7} - 3^{5} + 3^{4} - 3^{2} =
7^{4} - 7^{3} - 7^{2} + 7^{1} =
13^{3} - 13^{2} - 13^{1} + 13^{0}.

•
2016 can be written as 6!!(6!!-6).

2016 has 36 divisors (see below), whose sum is σ = 6552. Its totient is φ = 576.

The previous prime is 2011. The next prime is 2017. The reversal of 2016 is 6102.

Adding to 2016 its reverse (6102), we get a palindrome (8118).

It can be divided in two parts, 20 and 16, that added together give a triangular number (36 = T_{8}).

2016 = 3^{3} + 4^{3} + ... + 9^{3}.

2016 is a nontrivial binomial coefficient, being equal to C(64, 2).

It is a tau number, because it is divible by the number of its divisors (36).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 2 and base 14.

It is a zygodrome in base 2.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 1989 and 2007.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 2016.

It is not an unprimeable number, because it can be changed into a prime (2011) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 285 + ... + 291.

It is an arithmetic number, because the mean of its divisors is an integer number (182).

2016 is the 63-rd triangular number and also the 32-nd hexagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 2016, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3276).

2016 is an abundant number, since it is smaller than the sum of its proper divisors (4536).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

2016 is a wasteful number, since it uses less digits than its factorization.

2016 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 9.

The square root of 2016 is about 44.8998886413. The cubic root of 2016 is about 12.6327191953.

The spelling of 2016 in words is "two thousand, sixteen".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 32 36 42 48 56 63 72 84 96 112 126 144 168 224 252 288 336 504 672 1008 2016

• e-mail: info -at- numbersaplenty.com • Privacy notice • done in 0.070 sec. • engine limits •