Wednesday, September 20, 2017

Number of the day: 129

Properties of the number 129:

129 = 3 × 43 is semiprime and squarefree.
129 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 84 totatives.
129 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 129 results in an emirpimes.
129 = 13 + 43 + 43 is the sum of 3 positive cubes in 1 way.
129 = 652 - 642 = 232 - 202 is the difference of 2 nonnegative squares in 2 ways.
129 is the difference of 2 positive pentagonal numbers in 1 way.
129 = 22 + 52 + 102 is the sum of 3 positive squares.
1292 is the sum of 3 positive squares.
129 is a proper divisor of 1732 - 1.
129 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 23, 24, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 45, 51, 55, 60, 69, 71, 72, 78, 80, 84, 89, 91, 93, 94, 98, and 100.
129 is palindromic in (at least) the following bases: 2, 6, 42, -7, -16, -32, and -64.
129 in base 6 = 333 and consists of only the digit '3'.

The number 129 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000051: a(n) = 2^n + 1.
A000930: Narayana's cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3).
A000959: Lucky numbers.
A001358: Semiprimes (or biprimes): products of two primes.
A001969: Evil numbers: numbers with an even number of 1's in their binary expansion.
A005408: The odd numbers: a(n) = 2*n + 1.
A006881: Squarefree semiprimes: Numbers that are the product of two distinct primes.
A007504: Sum of first n primes.
A008585: a(n) = 3*n.
A016813: a(n) = 4n + 1.

No comments:

Post a Comment