Tuesday, March 13, 2018

Number of the day: 171

Properties of the number 171:

171 = 32 × 19 is the 131th composite number and is not squarefree.
171 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 108 totatives.
171 has a semiprime digit sum 9 in base 10.
171 has a prime digit product 7 in base 10.
171 = 862 - 852 = 302 - 272 = 142 - 52 is the difference of 2 nonnegative squares in 3 ways.
171 = (18 × 19)/2 is a triangular number.
171 is the difference of 2 positive pentagonal numbers in 1 way.
171 = 12 + 72 + 112 is the sum of 3 positive squares.
1712 is the sum of 3 positive squares.
171 is a proper divisor of 372 - 1.
171 is a palindrome (in base 10).
171 is palindromic in (at least) the following bases: 7, 18, 56, -2, -8, -17, -34, and -85.
171 in base 4 = 2223 and consists of only the digits '2' and '3'.
171 in base 5 = 1141 and consists of only the digits '1' and '4'.
171 in base 6 = 443 and consists of only the digits '3' and '4'.
171 in base 7 = 333 and consists of only the digit '3'.
171 consists of only the digits '1' and '7'.

The number 171 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000217: Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n.
A000959: Lucky numbers.
A001045: Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1.
A002113: Palindromes in base 10.
A004767: a(n) = 4*n + 3.
A005349: Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
A008585: a(n) = 3*n.
A014105: Second hexagonal numbers: a(n) = n*(2n+1).
A014612: Numbers that are the product of exactly three (not necessarily distinct) primes.
A139250: Toothpick sequence (see Comments lines for definition).

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