34992 has 40 divisors (see below), whose sum is σ = 101680. Its totient is φ = 11664.

The previous prime is 34981. The next prime is 35023. The reversal of 34992 is 29943.

Multipling 34992 by its sum of digits (27), we get a square (944784 = 972^{2}).

34992 divided by its sum of digits (27) gives a 4-th power (1296 = 6^{4}).

It can be divided in two parts, 349 and 92, that added together give a square (441 = 21^{2}).

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a nialpdrome in base 6, base 9 and base 14.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 34992.

It is an unprimeable number.

34992 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 (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 11663 + 11664 + 11665.

It is an arithmetic number, because the mean of its divisors is an integer number (2542).

34992 is a Friedman number, since it can be written as (3*(9*2)^4)/9, using all its digits and the basic arithmetic operations.

2^{34992} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34992, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50840).

34992 is an abundant number, since it is smaller than the sum of its proper divisors (66688).

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

34992 is an frugal number, since it uses more digits than its factorization.

34992 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 29 (or 5 counting only the distinct ones).

The product of its digits is 1944, while the sum is 27.

The square root of 34992 is about 187.0614872174. The cubic root of 34992 is about 32.7081706710.

The spelling of 34992 in words is "thirty-four thousand, nine hundred ninety-two".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 81 108 144 162 216 243 324 432 486 648 729 972 1296 1458 1944 2187 2916 3888 4374 5832 8748 11664 17496 34992

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