Tuesday, October 24, 2017

Number of the day: 268

Properties of the number 268:

268 = 22 × 67 is the 211th composite number and is not squarefree.
268 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 132 totatives.
Reversing the decimal digits of 268 results in a semiprime.
268 = 682 - 662 is the difference of 2 nonnegative squares in 1 way.
268 is the sum of 2 positive triangular numbers.
268 is the difference of 2 positive pentagonal numbers in 1 way.
268 = 62 + 62 + 142 is the sum of 3 positive squares.
2682 is the sum of 3 positive squares.
268 is a proper divisor of 4012 - 1.
268 is palindromic in (at least) the following bases: 8, 66, -14, and -89.
268 in base 8 = 414 and consists of only the digits '1' and '4'.
268 in base 11 = 224 and consists of only the digits '2' and '4'.

The number 268 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001043: Numbers that are the sum of 2 successive primes.
A002371: Period of decimal expansion of 1/(n-th prime) (0 by convention for the primes 2 and 5).
A002822: Numbers n such that 6n-1, 6n+1 are twin primes.
A005114: Untouchable numbers, also called nonaliquot numbers: impossible values for sum of aliquot parts of n (A001065).
A006093: a(n) = prime(n) - 1.
A014263: Numbers that contain even digits only.
A016957: a(n) = 6*n + 4.
A017113: a(n) = 8*n+4.
A054753: Numbers which are the product of a prime and the square of a different prime (p^2 * q).
A246392: Numbers n such that Phi(10, n) is prime, where Phi is the cyclotomic polynomial.

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