Number of the day: 3009

Axel Thue was born on this day 158 years ago.

Properties of the number 3009:

3009 is a cyclic number.
3009 = 3 × 17 × 59 is a sphenic number and squarefree.
3009 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 1856 totatives.
3009 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3009 results in a semiprime.
3009 = 1505² - 1504² = 503² - 500² = 97² - 80² = 55² - 4² is the difference of 2 nonnegative squares in 4 ways.
3009 is the sum of 2 positive triangular numbers.
3009 is the difference of 2 positive pentagonal numbers in 1 way.
3009 = 5² + 22² + 50² is the sum of 3 positive squares.
3009² = 1416² + 2655² is the sum of 2 positive squares in 1 way.
3009² is the sum of 3 positive squares.
3009 is a proper divisor of 353⁴ - 1.
3009 is palindromic in (at least) the following bases: 21, 47, 58, -64, and -94.
3009 in base 3 = 11010110 and consists of only the digits '0' and '1'.
3009 in base 21 = 6h6 and consists of only the digits '6' and 'h'.
3009 in base 24 = 559 and consists of only the digits '5' and '9'.
3009 in base 46 = 1JJ and consists of only the digits '1' and 'J'.
3009 in base 47 = 1H1 and consists of only the digits '1' and 'H'.
3009 in base 54 = 11d and consists of only the digits '1' and 'd'.

The number 3009 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000065: -1 + number of partitions of n.
A001402: Number of partitions of n into at most 6 parts.
A007202: Crystal ball sequence for hexagonal close-packing.
A015882: Numbers n such that sigma(n) = sigma(n + 12).
A026812: Number of partitions of n in which the greatest part is 6.
A051876: 24-gonal numbers: a(n) = n*(11*n-10).
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A056105: First spoke of a hexagonal spiral.
A256709: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 9 as largest digit.
A303814: Generalized 24-gonal (or icositetragonal) numbers: m*(11*m - 10) with m = 0, +1, -1, +2, -2, +3, -3, ...