Number of the day: 46585

Elwyn Ralph Berlekamp was born on this day 80 years ago.

Properties of the number 46585:

46585 = 5 × 7 × 11³ is the 41771^th composite number and is not squarefree.
46585 has 3 distinct prime factors, 16 divisors, 21 antidivisors and 29040 totatives.
46585 has a triangular digit sum 28 in base 10.
46585 = 60² + … + 70² is the sum of at least 2 consecutive positive squares in 1 way.
46585 = 33³ + 22³ is the sum of 2 positive cubes in 1 way.
46585 = (134 × 135)/2 + … + (138 × 139)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
46585 = 23293² - 23292² = 4661² - 4656² = 3331² - 3324² = 2123² - 2112² = 683² - 648² = 451² - 396² = 341² - 264² = 253² - 132² is the difference of 2 nonnegative squares in 8 ways.
46585 is the difference of 2 positive pentagonal numbers in 8 ways.
46585 = 37² + 60² + 204² is the sum of 3 positive squares.
46585² = 27951² + 37268² is the sum of 2 positive squares in 1 way.
46585² is the sum of 3 positive squares.
46585 is a proper divisor of 727⁴⁴ - 1.
46585 is palindromic in (at least) the following bases: 71, and -69.
46585 in base 49 = JJZ and consists of only the digits 'J' and 'Z'.

The number 46585 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A013618: Triangle of coefficients in expansion of (1+11x)^n.
A033445: a(n) = (n - 1)*(n^2 + n - 1).
A038315: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*1^j.
A057965: Triangle T(n,k) of number of minimal 4-covers of a labeled n-set that cover k points of that set uniquely (k=4,..,n).
A120075: Row sums of triangle A120073 (denominator triangle for H atom spectrum).
A192100: Table read by rows of numbers of unordered pairs of partitions of n-element set that have Rand distance k (n>=2, 1 <= k <= n(n-1)/2.
A261640: Numbers n such that both the digital sum of n is the same as the digital sum of n^2 in both base 2 and base 10.
A267233: Number of length-4 0..n arrays with no following elements greater than or equal to the first repeated value.
A325179: Heinz numbers of integer partitions such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.