Number of the day: 2005

Peter Gustav Lejeune Dirichlet was born on this day 216 years ago.

Properties of the number 2005:

2005 = 5 × 401 is semiprime and squarefree.
2005 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 1600 totatives.
2005 has a prime digit sum 7 in base 10.
Reversing the decimal digits of 2005 results in a sphenic number.
2005 = 1003² - 1002² = 203² - 198² is the difference of 2 nonnegative squares in 2 ways.
2005 is the sum of 2 positive triangular numbers.
2005 is the difference of 2 positive pentagonal numbers in 2 ways.
2005 = 22² + 39² = 18² + 41² is the sum of 2 positive squares in 2 ways.
2005 = 4² + 15² + 42² is the sum of 3 positive squares.
2005² = 1357² + 1476² = 1203² + 1604² = 1037² + 1716² = 200² + 1995² is the sum of 2 positive squares in 4 ways.
2005² is the sum of 3 positive squares.
2005 is a proper divisor of 421⁴ - 1.
2005 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 8, 9, 15, 17, 19, 21, 22, 23, 27, 31, 32, 33, 34, 35, 37, 40, 41, 42, 44, 45, 46, 48, 49, 52, 53, 54, 55, 59, 61, 67, 69, 73, 74, 75, 78, 79, 84, 87, 91, 93, 94, and 99.
2005 is palindromic in (at least) the following bases: 20, -18, -20, -23, and -26.
2005 in base 4 = 133111 and consists of only the digits '1' and '3'.
2005 in base 12 = 11b1 and consists of only the digits '1' and 'b'.
2005 in base 13 = bb3 and consists of only the digits '3' and 'b'.
2005 in base 14 = a33 and consists of only the digits '3' and 'a'.
2005 in base 19 = 5aa and consists of only the digits '5' and 'a'.
2005 in base 20 = 505 and consists of only the digits '0' and '5'.
2005 in base 22 = 433 and consists of only the digits '3' and '4'.
2005 in base 25 = 355 and consists of only the digits '3' and '5'.
2005 in base 31 = 22l and consists of only the digits '2' and 'l'.
2005 in base 44 = 11P and consists of only the digits '1' and 'P'.

The number 2005 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014915: a(1)=1, a(n) = n*3^(n-1) + a(n-1).
A050993: 5-Kndel numbers.
A053701: Vertically symmetric numbers.
A098645: List the positions of all digits '1' in the sequence. This is the lexicographically earliest increasing sequence with this property.
A138993: a(n) = Frobenius number for 7 successive primes = F[p(n),p(n+1),p(n+2),p(n+3),p(n+4),p(n+5),p(n+6)].
A177814: Numbers n such that n^3 divides 14^(n^2)+1.
A193842: Triangular array: the fission of the polynomial sequence ((x+1)^n: n >= 0) by the polynomial sequence ((x+2)^n: n >= 0). (Fission is defined at Comments.)
A256631: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.
A292450: Numbers where 0 outnumbers any other digit.
A293880: Numbers having '20' as substring of their digits.