## Marius Sophus Lie was born on this day 174 years ago.

### Properties of the number 6826:

6826 = 2 × 3413 is semiprime and squarefree.6826 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 3412 totatives.

6826 has a semiprime digit sum 22 in base 10.

Reversing the decimal digits of 6826 results in a sphenic number.

6826 is the difference of 2 positive pentagonal numbers in 2 ways.

6826 = 51

^{2}+ 65

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

6826 = 24

^{2}+ 25

^{2}+ 75

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

6826

^{2}= 1624

^{2}+ 6630

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

6826

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

6826 is a divisor of 1471

^{4}- 1.

6826 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 8, 11, 14, 15, 18, 22, 29, 30, 36, 42, 44, 46, 49, 51, 54, 55, 56, 57, 59, 63, 69, 70, 73, 78, 80, 84, 86, 89, 91, and 98.

6826 is palindromic in (at least) the following bases: 65, 75, -4, -8, and -91.

6826 in base 4 = 1222222 and consists of only the digits '1' and '2'.

6826 in base 16 = 1aaa and consists of only the digits '1' and 'a'.

6826 in base 27 = 99m and consists of only the digits '9' and 'm'.

### The number 6826 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A004250: Number of partitions of n into 3 or more parts.

A020989: (5*4^n-2)/3.

A041227: Denominators of continued fraction convergents to sqrt(125).

A061547: Number of 132 and 213-avoiding derangements of {1,2,...,n}.

A081254: Numbers n such that A081252(m)/m^2 has a local maximum for m = n.

A084170: a(n) = 5*2^n/3 + (-1)^n/3 - 1.

A084214: Inverse binomial transform of a math magic problem.

A112739: Array counting nodes in rooted trees of height n in which the root and internal nodes have valency k (and the leaf nodes have valency one).

A162316: a(n) = 5n^2 + 20n + 1.

A239481: Number of partitions p of n such that if h = 2*min(p), then h is an (h,2)-separator of p; see Comments.

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