Sunday, March 19, 2017

Number of the day: 282

Properties of the number 282:

282 = 2 × 3 × 47 is a sphenic number and squarefree.
282 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 92 totatives.
282 has an oblong digit sum 12 in base 10.
282 = (3 × 4)/2 + … + (11 × 12)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
282 is the sum of 2 positive triangular numbers.
282 is the difference of 2 positive pentagonal numbers in 2 ways.
282 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
282 = 72 + 82 + 132 is the sum of 3 positive squares.
2822 is the sum of 3 positive squares.
282 is a divisor of 2812 - 1.
282 is a palindrome (in base 10).
282 is palindromic in (at least) the following bases: 5, 9, 46, 93, and -14.
282 in base 3 = 101110 and consists of only the digits '0' and '1'.
282 in base 5 = 2112 and consists of only the digits '1' and '2'.
282 in base 7 = 552 and consists of only the digits '2' and '5'.
282 in base 9 = 343 and consists of only the digits '3' and '4'.
282 consists of only the digits '2' and '8'.
282 in base 16 = 11a and consists of only the digits '1' and 'a'.

The number 282 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000219: Number of planar partitions of n.
A002113: Palindromes in base 10.
A002445: Denominators of Bernoulli numbers B_{2n}.
A002858: Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.
A005836: Numbers n whose base 3 representation contains no 2.
A007304: Sphenic numbers: products of 3 distinct primes.
A008864: a(n) = prime(n) + 1.
A014574: Average of twin prime pairs.
A024675: Average of two consecutive odd primes.
A027642: Denominator of Bernoulli number B_n.

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