### Properties of the number 6545:

6545 = 5 × 7 × 11 × 17 is the 5700^{th}composite number and is squarefree.

6545 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 3840 totatives.

6545 has an oblong digit sum 20 in base 10.

6545 has an oblong digit product 600 in base 10.

6545 = 11

^{2}+ … + 27

^{2}is the sum of at least 2 consecutive positive squares in 1 way.

6545 = (1 × 2)/2 + … + (33 × 34)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.

6545 = 3273

^{2}- 3272

^{2}= 657

^{2}- 652

^{2}= 471

^{2}- 464

^{2}= 303

^{2}- 292

^{2}= 201

^{2}- 184

^{2}= 111

^{2}- 76

^{2}= 87

^{2}- 32

^{2}= 81

^{2}- 4

^{2}is the difference of 2 nonnegative squares in 8 ways.

6545 is the sum of 2 positive triangular numbers.

6545 is the difference of 2 positive pentagonal numbers in 6 ways.

6545 = 10

^{2}+ 19

^{2}+ 78

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

6545

^{2}= 3080

^{2}+ 5775

^{2}= 1001

^{2}+ 6468

^{2}= 2772

^{2}+ 5929

^{2}= 3927

^{2}+ 5236

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

6545

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

6545 is a divisor of 1429

^{2}- 1.

6545 = '6' + '545' is the concatenation of 2 semiprime numbers.

6545 is palindromic in (at least) the following bases: 16, 21, 84, and -23.

6545 in base 16 = 1991 and consists of only the digits '1' and '9'.

6545 in base 21 = ehe and consists of only the digits 'e' and 'h'.

6545 in base 22 = dbb and consists of only the digits 'b' and 'd'.

### The number 6545 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A000292: Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.

A000447: a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.

A013594: Smallest order of cyclotomic polynomial containing n or -n as a coefficient.

A092269: Spt function: total number of smallest parts in all partitions of n.

A134605: Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.

A135602: Right-angled numbers with an internal digit as the vertex.

A138135: Number of parts > 1 in the last section of the set of partitions of n.

A152977: Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the number of partitions of 2^n into powers of 2 less than or equal to 2^k.

A248068: T(n,k)=Number of length n+5 0..k arrays with some disjoint triples in each consecutive six terms having the same sum

A255872: Smallest Rhonda number to base b = n-th composite number, cf. A002808.

## No comments:

## Post a Comment