1536 has 20 divisors (see below), whose sum is σ = 4092. Its totient is φ = 512.

The previous prime is 1531. The next prime is 1543. The reversal of 1536 is 6351.

Adding to 1536 its sum of digits (15), we get a palindrome (1551).

Subtracting from 1536 its sum of digits (15), we obtain a square (1521 = 39^{2}).

Adding to 1536 its reverse (6351), we get a palindrome (7887).

1536 = T_{3} + T_{4} + ... +
T_{20}.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (2!)^{6}.

1536 is nontrivially palindromic in base 15.

1536 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is an ABA number since it can be written as A⋅B^{A}, here for A=3, B=8.

It is an Ulam number.

1536 is an undulating number in base 15.

Its product of digits (90) is a multiple of the sum of its prime divisors (5).

It is a plaindrome in base 11.

It is a nialpdrome in base 2, base 8, base 12 and base 16.

It is a zygodrome in base 2 and base 11.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 1536.

It is not an unprimeable number, because it can be changed into a prime (1531) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

In principle, a polygon with 1536 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 511 + 512 + 513.

1536 is a gapful number since it is divisible by the number (16) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1536, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2046).

1536 is an abundant number, since it is smaller than the sum of its proper divisors (2556).

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

1536 is an frugal number, since it uses more digits than its factorization.

1536 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21 (or 5 counting only the distinct ones).

The product of its digits is 90, while the sum is 15.

The square root of 1536 is about 39.1918358845. The cubic root of 1536 is about 11.5379965625.

The spelling of 1536 in words is "one thousand, five hundred thirty-six".

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