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1729 = 71319
BaseRepresentation
bin11011000001
32101001
4123001
523404
612001
75020
oct3301
92331
101729
111332
121001
13a30
148b7
157a4
hex6c1

1729 has 8 divisors (see below), whose sum is σ = 2240. Its totient is φ = 1296.

The previous prime is 1723. The next prime is 1733. The reversal of 1729 is 9271.

1729 divided by its sum of digits (19) gives a triangular number (91 = T13).

It can be divided in two parts, 172 and 9, that added together give a palindrome (181).

1729 = 93 + 103.

1729 is nontrivially palindromic in base 12.

It is a Cunningham number, because it is equal to 123+1.

It is a sphenic number, since it is the product of 3 distinct primes.

It is a 2-Lehmer number, since φ(1729) divides (1729-1)2.

It is a cyclic number.

It is a Carmichael number.

It is not a de Polignac number, because 1729 - 23 = 1721 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (19).

It is a deceptive number, since it divides R1728.

It is a taxicab number since it can be written as a sum of two cubes in more than one way. Here 1729 = 13 + 123 = 93 + 103.

It is a nialpdrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (1721) by changing a digit.

It is a Zeisel number, with parameters (1, 6).

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 82 + ... + 100.

It is an arithmetic number, because the mean of its divisors is an integer number (280).

It is a Proth number, since it is equal to 27 ⋅ 26 + 1 and 27 < 26.

It is a Poulet number, since it divides 21728-1.

1729 is a gapful number since it is divisible by the number (19) formed by its first and last digit.

It is an amenable number.

1729 is a deficient number, since it is larger than the sum of its proper divisors (511).

1729 is a wasteful number, since it uses less digits than its factorization.

1729 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39.

The product of its digits is 126, while the sum is 19.

The square root of 1729 is about 41.5812457726. The cubic root of 1729 is about 12.0023143684.

The spelling of 1729 in words is "one thousand, seven hundred twenty-nine".

Divisors: 1 7 13 19 91 133 247 1729