Number of the day: 6165

Properties of the number 6165:

6165 = 3² × 5 × 137 is the 5361^th composite number and is not squarefree.
6165 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 3264 totatives.
6165 = (30 × 31)/2 + … + (39 × 40)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6165 = 3083² - 3082² = 1029² - 1026² = 619² - 614² = 347² - 338² = 213² - 198² = 91² - 46² is the difference of 2 nonnegative squares in 6 ways.
6165 is the difference of 2 positive pentagonal numbers in 1 way.
6165 = 54² + 57² = 9² + 78² is the sum of 2 positive squares in 2 ways.
6165 = 10² + 17² + 76² is the sum of 3 positive squares.
6165² = 3960² + 4725² = 333² + 6156² = 1404² + 6003² = 3699² + 4932² is the sum of 2 positive squares in 4 ways.
6165² is the sum of 3 positive squares.
6165 is a divisor of 37⁴ - 1.
6165 is palindromic in (at least) the following bases: 35, 67, -27, and -92.
6165 in base 26 = 933 and consists of only the digits '3' and '9'.
6165 in base 34 = 5bb and consists of only the digits '5' and 'b'.
6165 in base 35 = 515 and consists of only the digits '1' and '5'.
6165 in base 55 = 225 and consists of only the digits '2' and '5'.

The number 6165 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045944: Rhombic matchstick numbers: n*(3*n+2).
A061541: Number of connected labeled graphs with n nodes and n+2 edges.
A062734: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, 0 <= k <= n(n-1)/2).
A073399: Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073400.
A123527: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, n-1 <= k <= n(n-1)/2).
A164000: Main diagonal of array in A163280.
A166512: 2-comma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for two different splittings n=concat(S[0],S[1]).
A214359: Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
A228024: Antiharmonic mean of the divisors of A228023(n) (the n-th primitive antiharmonic number).
A262521: Numbers where A262520 takes a negative value; numbers n for which A155043(2n) > A155043(2n + 1).