1540 has 24 divisors (see below), whose sum is σ = 4032. Its totient is φ = 480.

The previous prime is 1531. The next prime is 1543. The reversal of 1540 is 451.

1540 = T_{1} + T_{2} + ... +
T_{20}.

1540 is an esthetic number in base 9, because in such base its adjacent digits differ by 1.

1540 is a nontrivial binomial coefficient, being equal to C(56, 2), and to C(22, 3).

It is a Harshad number since it is a multiple of its sum of digits (10).

It is a nialpdrome in base 7 and base 12.

It is not an unprimeable number, because it can be changed into a prime (1543) by changing a digit.

It is the 20-th tetrahedral number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 135 + ... + 145.

It is an arithmetic number, because the mean of its divisors is an integer number (168).

1540 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1540 is the 55-th triangular number, the 28-th hexagonal number and also the 20-th decagonal number.

1540 is the 19-th centered nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1540, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2016).

1540 is an abundant number, since it is smaller than the sum of its proper divisors (2492).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

1540 is a wasteful number, since it uses less digits than its factorization.

1540 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 25 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 10.

The square root of 1540 is about 39.2428337407. The cubic root of 1540 is about 11.5480035029.

Multiplying 1540 by its sum of digits (10), we get a triangular number (15400 = T_{175}).

1540 divided by its product of nonzero digits (20) gives a palindrome (77).

Adding to 1540 its reverse (451), we get a palindrome (1991).

Subtracting from 1540 its reverse (451), we obtain a square (1089 = 33^{2}).

It can be divided in two parts, 15 and 40, that added together give a palindrome (55).

The spelling of 1540 in words is "one thousand, five hundred forty".

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