Number of the day: 6000

Alexander Grothendieck was born on this day 91 years ago.

Properties of the number 6000:

6000 = 2⁴ × 3 × 5³ is the 5216^th composite number and is not squarefree.
6000 has 3 distinct prime factors, 40 divisors, 13 antidivisors and 1600 totatives.
6000 has a semiprime digit sum 6 in base 10.
6000 has a triangular digit sum 6 in base 10.
6000 has an oblong digit sum 6 in base 10.
6000 = 8³ + 14³ + 14³ is the sum of 3 positive cubes in 1 way.
6000 = (19 × 20)/2 + … + (34 × 35)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6000 is the difference of 2 nonnegative squares in 12 ways.
6000 is the sum of 2 positive triangular numbers.
6000 is the difference of 2 positive pentagonal numbers in 1 way.
6000 is not the sum of 3 positive squares.
6000² = 3600² + 4800² = 1680² + 5760² = 2112² + 5616² is the sum of 2 positive squares in 3 ways.
6000² is the sum of 3 positive squares.
6000 is a proper divisor of 751² - 1.
6000 = '600' + '0' is the concatenation of 2 oblong numbers.
6000 is palindromic in (at least) the following bases: 79, 99, and -28.
6000 in base 3 = 22020020 and consists of only the digits '0' and '2'.
6000 consists of only the digits '0' and '6'.
6000 in base 14 = 2288 and consists of only the digits '2' and '8'.
6000 in base 20 = f00 and consists of only the digits '0' and 'f'.
6000 in base 24 = aa0 and consists of only the digits '0' and 'a'.
6000 in base 27 = 866 and consists of only the digits '6' and '8'.

The number 6000 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006933: 'Eban' numbers (the letter 'e' is banned!).
A018834: Numbers k such that decimal expansion of k^2 contains k as a substring.
A030283: a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).
A037124: Numbers that contain only one nonzero digit.
A057088: Scaled Chebyshev U-polynomials evaluated at i*sqrt(5)/2. Generalized Fibonacci sequence.
A084647: Hypotenuses for which there exist exactly 3 distinct integer triangles.
A132269: Product{k>=0, 1+floor(n/2^k)}.
A134605: Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.
A238556: Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.
A256633: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 6 as largest digit.