Saturday, November 11, 2017

Number of the day: 242

Properties of the number 242:

242 = 2 × 112 is the 188th composite number and is not squarefree.
242 has 2 distinct prime factors, 6 divisors, 10 antidivisors and 110 totatives.
242 has a Fibonacci digit sum 8 in base 10.
242 has sum of divisors equal to 399 which is a sphenic number.
242 = 35 - 15 is the difference of 2 positive fifth powers in 1 way.
242 is the difference of 2 positive pentagonal numbers in 1 way.
242 = 112 + 112 is the sum of 2 positive squares in 1 way.
242 = 12 + 42 + 152 is the sum of 3 positive squares.
2422 is the sum of 3 positive squares.
242 is a proper divisor of 2412 - 1.
242 = '2' + '42' is the concatenation of 2 oblong numbers.
242 is a palindrome (in base 10).
242 is palindromic in (at least) the following bases: 3, 7, 21, -12, and -15.
242 in base 3 = 22222 and consists of only the digit '2'.
242 in base 7 = 464 and consists of only the digits '4' and '6'.
242 in base 9 = 288 and consists of only the digits '2' and '8'.
242 consists of only the digits '2' and '4'.
242 in base 11 = 200 and consists of only the digits '0' and '2'.
242 in base 15 = 112 and consists of only the digits '1' and '2'.

The number 242 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000982: a(n) = ceiling(n^2/2).
A001105: a(n) = 2*n^2.
A002088: Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010.
A002113: Palindromes in base 10.
A002822: Numbers n such that 6n-1, 6n+1 are twin primes.
A008593: Multiples of 11.
A008864: a(n) = prime(n) + 1.
A014612: Numbers that are the product of exactly three (not necessarily distinct) primes.
A028982: Squares and twice squares.
A269303: Numbers n such that (266*10^n+1)/3 is prime.

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