1681 has 3 divisors (see below), whose sum is σ = 1723. Its totient is φ = 1640.

The previous prime is 1669. The next prime is 1693. The reversal of 1681 is 1861.

1681 = T_{40} + T_{41}.

The square root of 1681 is 41.

It is a perfect power (a square), and thus also a powerful number.

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length.

It is an interprime number because it is at equal distance from previous prime (1669) and next prime (1693).

It can be written as a sum of positive squares in only one way, i.e., 81 + 1600 = 9^2 + 40^2 .

It is not a de Polignac number, because 1681 - 2^{7} = 1553 is a prime.

It is a super-2 number, since 2×1681^{2} = 5651522, which contains 22 as substring.

It is a Duffinian number.

It is a plaindrome in base 9 and base 11.

It is a nialpdrome in base 8, base 12, base 14 and base 15.

It is not an unprimeable number, because it can be changed into a prime (1601) by changing a digit.

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 2 ways as a sum of consecutive naturals, for example, 21 + ... + 61.

1681 is the 41-st square number.

1681 is the 21-st centered octagonal number.

It is an amenable number.

1681 is a deficient number, since it is larger than the sum of its proper divisors (42).

1681 is an frugal number, since it uses more digits than its factorization.

1681 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82 (or 41 counting only the distinct ones).

The product of its digits is 48, while the sum is 16.

The cubic root of 1681 is about 11.8902021369.

Multiplying 1681 by its sum of digits (16), we get a square (26896 = 164^{2}).

It can be divided in two parts, 168 and 1, that added together give a square (169 = 13^{2}).

The spelling of 1681 in words is "one thousand, six hundred eighty-one".

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