Number of the day: 7851

Luitzen Egbertus Jan Brouwer was born on this day 138 years ago.

Properties of the number 7851:

7851 = 3 × 2617 is semiprime and squarefree.
7851 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 5232 totatives.
7851 has a semiprime digit sum 21 in base 10.
7851 has a Fibonacci digit sum 21 in base 10.
7851 has a triangular digit sum 21 in base 10.
7851 = 3926² - 3925² = 1310² - 1307² is the difference of 2 nonnegative squares in 2 ways.
7851 is the difference of 2 positive pentagonal numbers in 1 way.
7851 = 1² + 25² + 85² is the sum of 3 positive squares.
7851² = 1224² + 7755² is the sum of 2 positive squares in 1 way.
7851² is the sum of 3 positive squares.
7851 is a proper divisor of 1553⁶ - 1.
7851 is an emirpimes in (at least) the following bases: 3, 5, 8, 11, 15, 18, 20, 24, 30, 35, 37, 51, 53, 59, 63, 66, 67, 68, 69, 70, 73, 74, 78, 82, 85, 89, 90, 91, 93, and 97.
7851 is palindromic in (at least) the following bases: 31, and -21.
7851 in base 29 = 99l and consists of only the digits '9' and 'l'.
7851 in base 30 = 8ll and consists of only the digits '8' and 'l'.
7851 in base 31 = 858 and consists of only the digits '5' and '8'.
7851 in base 62 = 22d and consists of only the digits '2' and 'd'.

The number 7851 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A063052: Integers n > 879 such that the 'Reverse and Add!' trajectory of n joins the trajectory of 879.
A084449: Positions of sevens (ground states) in A084451.
A120006: Expansion of ((eta(q^2) * eta(q^14)) / (eta(q) * eta(q^7)))^3 in powers of q.
A123648: Expansion of eta(q^4) * eta(q^28) / (eta(q) * eta(q^7)) in powers of q.
A125522: A 4 x 4 permutation-free magic square.
A127873: a(n) = (n^3)/2 + (3*n^2)/2 + 3*n + 3.
A145169: G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x)^3.
A231710: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to one
A240209: Number of partitions p of n such that median(p) = multiplicity(max(p)).
A240671: Floor(4^n/(2+2*cos(2*Pi/7))^n).