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133728 = 2537199
BaseRepresentation
bin100000101001100000
320210102220
4200221200
513234403
62511040
71064610
oct405140
9223386
10133728
1191521
1265480
1348b3a
1436a40
1529953
hex20a60

133728 has 48 divisors (see below), whose sum is σ = 403200. Its totient is φ = 38016.

The previous prime is 133723. The next prime is 133733. The reversal of 133728 is 827331.

It is an interprime number because it is at equal distance from previous prime (133723) and next prime (133733).

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-3 number, since 3×1337283 = 7174444876333056, which contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nude number because it is divisible by every one of its digits.

It is a d-powerful number, because it can be written as 1 + 3 + 74 + 35 + 217 + 8 .

It is a junction number, because it is equal to n+sod(n) for n = 133698 and 133707.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (133723) by changing a digit.

133728 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, 573 + ... + 771.

It is an arithmetic number, because the mean of its divisors is an integer number (8400).

2133728 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 133728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (201600).

133728 is an abundant number, since it is smaller than the sum of its proper divisors (269472).

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

133728 is a wasteful number, since it uses less digits than its factorization.

133728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 219 (or 211 counting only the distinct ones).

The product of its digits is 1008, while the sum is 24.

The square root of 133728 is about 365.6883919405. The cubic root of 133728 is about 51.1376519720.

It can be divided in two parts, 133 and 728, that added together give a triangular number (861 = T41).

The spelling of 133728 in words is "one hundred thirty-three thousand, seven hundred twenty-eight".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 84 96 112 168 199 224 336 398 597 672 796 1194 1393 1592 2388 2786 3184 4179 4776 5572 6368 8358 9552 11144 16716 19104 22288 33432 44576 66864 133728