Sunday, May 1, 2016

Number of the day: 639

Properties of the number 639:

639 = 32 × 71 is the 523th composite number and is not squarefree.
639 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 420 totatives.
639 = 3202 - 3192 = 1082 - 1052 = 402 - 312 is the difference of 2 nonnegative squares in 3 ways.
639 is the sum of 2 positive triangular numbers.
639 is the difference of 2 positive pentagonal numbers in 1 way.
639 is not the sum of 3 positive squares.
6392 is the sum of 3 positive squares.
639 is a divisor of 12772 - 1.
639 = '6' + '39' is the concatenation of 2 semiprime numbers.
639 is palindromic in (at least) the following bases: 22, and 70.
639 in base 8 = 1177 and consists of only the digits '1' and '7'.
639 in base 14 = 339 and consists of only the digits '3' and '9'.
639 in base 21 = 199 and consists of only the digits '1' and '9'.
639 in base 22 = 171 and consists of only the digits '1' and '7'.

The number 639 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002893: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2k,k).
A006884: In the `3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.
A007504: Sum of first n primes.
A040040: Average of twin prime pairs (A014574), divided by 2. Equivalently, 2*a(n)-1 and 2*a(n)+1 are primes.
A060980: |First digit - second digit + third digit - fourth digit ...| = 12.
A087097: Lunar primes (formerly called dismal primes) (cf. A087062).
A117817: Let T_n be the infinite sequence formed by starting with 1 and repeatedly reversing the digits and adding n to get the next term. If T_n eventually reaches a cycle, sequence gives length of that cycle, otherwise -1.
A121029: Multiples of 9 containing a 9 in their decimal representation.
A187220: Gullwing sequence (see Comments lines for precise definition).
A235228: Numbers whose sum of digits is 18.

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