### Properties of the number 6165:

6165 = 3^{2}× 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 = 3083

^{2}- 3082

^{2}= 1029

^{2}- 1026

^{2}= 619

^{2}- 614

^{2}= 347

^{2}- 338

^{2}= 213

^{2}- 198

^{2}= 91

^{2}- 46

^{2}is the difference of 2 nonnegative squares in 6 ways.

6165 is the difference of 2 positive pentagonal numbers in 1 way.

6165 = 54

^{2}+ 57

^{2}= 9

^{2}+ 78

^{2}is the sum of 2 positive squares in 2 ways.

6165 = 10

^{2}+ 17

^{2}+ 76

^{2}is the sum of 3 positive squares.

6165

^{2}= 3960

^{2}+ 4725

^{2}= 333

^{2}+ 6156

^{2}= 1404

^{2}+ 6003

^{2}= 3699

^{2}+ 4932

^{2}is the sum of 2 positive squares in 4 ways.

6165

^{2}is the sum of 3 positive squares.

6165 is a divisor of 37

^{4}- 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).

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