Number of the day: 7735

André Weil was born on this day 113 years ago.

Properties of the number 7735:

7735 is a cyclic number.
7735 = 5 × 7 × 13 × 17 is the 6753^th composite number and is squarefree.
7735 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 4608 totatives.
7735 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 7735 results in a semiprime.
7735 = (26 × 27)/2 + … + (39 × 40)/2 = (6 × 7)/2 + … + (35 × 36)/2 is the sum of at least 2 consecutive triangular numbers in 2 ways.
7735 = 3868² - 3867² = 776² - 771² = 556² - 549² = 304² - 291² = 236² - 219² = 128² - 93² = 92² - 27² = 88² - 3² is the difference of 2 nonnegative squares in 8 ways.
7735 is the sum of 2 positive triangular numbers.
7735 is the difference of 2 positive pentagonal numbers in 6 ways.
7735 is not the sum of 3 positive squares.
7735² = 3640² + 6825² = 1183² + 7644² = 3276² + 7007² = 4032² + 6601² = 735² + 7700² = 5208² + 5719² = 4900² + 5985² = 329² + 7728² = 1848² + 7511² = 2975² + 7140² = 1904² + 7497² = 3927² + 6664² = 4641² + 6188² is the sum of 2 positive squares in 13 ways.
7735² is the sum of 3 positive squares.
7735 is a proper divisor of 1429² - 1.
7735 = '773' + '5' is the concatenation of 2 prime numbers.
7735 = '77' + '35' is the concatenation of 2 semiprime numbers.
7735 is palindromic in (at least) base 90.
7735 in base 23 = ee7 and consists of only the digits '7' and 'e'.
7735 in base 26 = bbd and consists of only the digits 'b' and 'd'.

The number 7735 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A032164: Number of aperiodic necklaces of n beads of 6 colors; dimensions of free Lie algebras.
A074650: Table T(n,k) read by downward antidiagonals: number of Lyndon words (aperiodic necklaces) with n beads of k colors, n >= 1, k >= 1.
A075147: Number of Lyndon words (aperiodic necklaces) with n beads of n colors.
A097102: Numbers n that are the hypotenuse of exactly 13 distinct integer-sided right triangles, i.e., n^2 can be written as a sum of two squares in 13 ways.
A116522: a(0)=1, a(1)=1, a(n)=7a(n/2) for n=2,4,6,..., a(n)=6a((n-1)/2)+a((n+1)/2) for n=3,5,7,....
A143325: Table T(n,k) by antidiagonals. T(n,k) is the number of length n primitive (=aperiodic or period n) k-ary words (n,k >= 1) which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A221578: A sum over partitions (q=6), see first comment.
A271580: Magic sums of 4 X 4 magic squares composed of squares.
A324315: Squarefree integers m > 1 such that if prime p divides m, then the sum of the base p digits of m is at least p.