Monday, March 14, 2016

Number of the day: 31416

In honor of Pi Day 2016 (3.14.16), today's number of the day is 31416 ( = 10000π rounded to an integer).

Properties of the number 31416:

31416 = 23 × 3 × 7 × 11 × 17 is composite.
31416 has 5 distinct prime factors, 64 divisors and 19 antidivisors.
31416 has a semiprime digit sum 15 in base 10.
31416 has a triangular digit sum 15 in base 10.
31416 has an oblong digit product 72 in base 10.
31416 is the difference of 2 nonnegative squares in 16 ways.
31416 is the sum of 3 positive squares.
314162 is the sum of 2 positive squares in 1 way.
31416 is palindromic in (at least) the following bases: 36, and 57.
31416 in base 33 = ss0 and consists of only the digits '0' and 's'.
31416 in base 36 = o8o and consists of only the digits '8' and 'o'.
31416 in base 38 = LSS and consists of only the digits 'L' and 'S'.
31416 in base 57 = 9c9 and consists of only the digits '9' and 'c'.

The number 31416 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011546: Decimal expansion of Pi rounded to n places.
A034323: a(n) = n-th quintic factorial number divided by 2.
A050780: (n + sopf_n = m) and (m - sopf_m = n). Sequence gives values of n.
A051799: Partial sums of A007587.
A067048: a(n) = lcm(n, n+1, n+2, n+3, n+4) / 60.
A181337: Number of even entries in the top rows of all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
A189984: Numbers with prime factorization pqrst^3.
A198438: Common differences in triples of squares in arithmetic progression, that are not a multiples of other triples in (A198384,A198385,A198386).
A212514: Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>3z.
A221590: T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their king-move neighbors in a random 0..3 nXk array