Saturday, June 25, 2016

Number of the day: 21368

Properties of the number 21368:

21368 = 23 × 2671 is the 18970th composite number and is not squarefree.
21368 has 2 distinct prime factors, 8 divisors, 31 antidivisors and 10680 totatives.
21368 has an oblong digit sum 20 in base 10.
21368 = 53432 - 53412 = 26732 - 26692 is the difference of 2 nonnegative squares in 2 ways.
21368 is the sum of 2 positive triangular numbers.
21368 = 42 + 62 + 1462 is the sum of 3 positive squares.
213682 is the sum of 3 positive squares.
21368 is a divisor of 3730 - 1.
21368 is palindromic in (at least) base -35.
21368 in base 13 = 9959 and consists of only the digits '5' and '9'.
21368 in base 34 = igg and consists of only the digits 'g' and 'i'.

The number 21368 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006601: Numbers n such that n, n+1, n+2 and n+3 have the same number of divisors.
A102186: The PDO(n) function (Partitions with Designated summands in which all parts are Odd): the sum of products of multiplicities of parts in all partitions of n into odd parts.
A108433: Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and have k hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).
A124401: Indices where 2 occurs in A124151.
A127936: Numbers n such that 1 + Sum_{i=1..n} 2^(2i-1) is prime.
A180249: a(n) is the total number of k-reverses of n.
A220031: Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 nX7 array
A238491: Number of partitions of n not containing 3*(number of parts) as a part.

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