137952 has 36 divisors (see below), whose sum is σ = 393120. Its totient is φ = 45888.

The previous prime is 137947. The next prime is 137957. The reversal of 137952 is 259731.

It is an interprime number because it is at equal distance from previous prime (137947) and next prime (137957).

It is a tau number, because it is divible by the number of its divisors (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137957) by changing a digit.

137952 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 49 + ... + 527.

It is an arithmetic number, because the mean of its divisors is an integer number (10920).

2¹³⁷⁹⁵² is an apocalyptic number.

137952 is a gapful number since it is divisible by the number (12) 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 137952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196560).

137952 is an abundant number, since it is smaller than the sum of its proper divisors (255168).

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

137952 is a wasteful number, since it uses less digits than its factorization.

137952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 495 (or 484 counting only the distinct ones).

The product of its digits is 1890, while the sum is 27.

The square root of 137952 is about 371.4189009730. The cubic root of 137952 is about 51.6705003514.

It can be divided in two parts, 1379 and 52, that added together give a triangular number (1431 = T₅₃).

The spelling of 137952 in words is "one hundred thirty-seven thousand, nine hundred fifty-two".