Tuesday, December 19, 2017

Number of the day: 2298

Properties of the number 2298:

2298 = 2 × 3 × 383 is a sphenic number and squarefree.
2298 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 764 totatives.
2298 has a semiprime digit sum 21 in base 10.
2298 has a Fibonacci digit sum 21 in base 10.
2298 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 2298 results in a sphenic number.
2298 is the sum of 2 positive triangular numbers.
2298 is the difference of 2 positive pentagonal numbers in 2 ways.
2298 = 52 + 82 + 472 is the sum of 3 positive squares.
22982 is the sum of 3 positive squares.
2298 is a proper divisor of 15312 - 1.
2298 is palindromic in (at least) the following bases: 27, 28, and -41.
2298 in base 3 = 10011010 and consists of only the digits '0' and '1'.
2298 in base 9 = 3133 and consists of only the digits '1' and '3'.
2298 in base 15 = a33 and consists of only the digits '3' and 'a'.
2298 in base 19 = 66i and consists of only the digits '6' and 'i'.
2298 in base 26 = 3aa and consists of only the digits '3' and 'a'.
2298 in base 27 = 343 and consists of only the digits '3' and '4'.
2298 in base 28 = 2q2 and consists of only the digits '2' and 'q'.
2298 in base 47 = 11g and consists of only the digits '1' and 'g'.

The number 2298 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A028878: a(n) = (n+3)^2 - 6.
A051228: Bernoulli number B_{n} has denominator 42.
A083096: Numbers n such that 3 divides sum(k=1,n, C(2k,k) ).
A084785: Diagonal of the triangle (A084783) and the self-convolution of the first column (A084784).
A090801: List of distinct numbers appearing as denominators of Bernoulli numbers.
A217729: Trajectory of 40 under the map n-> A006369(n).
A218038: Numbers n such that Q(sqrt(n)) has class number 6.
A225196: Number of 6-line partitions of n (i.e., planar partitions of n with at most 6 lines).
A269606: T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.
A270850: T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1, k or k-1 exactly once.

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