127008 has 90 divisors (see below), whose sum is σ = 434511. Its totient is φ = 36288.

The previous prime is 126989. The next prime is 127031. The reversal of 127008 is 800721.

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 can be written as a sum of positive squares in only one way, i.e., 63504 + 63504 = 252^2 + 252^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=252.

It is a super-2 number, since 2×127008^{2} = 32262064128, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 14 ways as a sum of consecutive naturals, for example, 18141 + ... + 18147.

2^{127008} is an apocalyptic number.

127008 is a gapful number since it is divisible by the number (18) 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 127008

127008 is an abundant number, since it is smaller than the sum of its proper divisors (307503).

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

127008 is an equidigital number, since it uses as much as digits as its factorization.

127008 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 18.

The square root of 127008 is about 356.3818177180. The cubic root of 127008 is about 50.2663123694.

Multiplying 127008 by its sum of digits (18), we get a square (2286144 = 1512^{2}).

127008 divided by its sum of digits (18) gives a square (7056 = 84^{2}).

Adding to 127008 its reverse (800721), we get a palindrome (927729).

The spelling of 127008 in words is "one hundred twenty-seven thousand, eight".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 49 54 56 63 72 81 84 96 98 108 112 126 144 147 162 168 189 196 216 224 252 288 294 324 336 378 392 432 441 504 567 588 648 672 756 784 864 882 1008 1134 1176 1296 1323 1512 1568 1764 2016 2268 2352 2592 2646 3024 3528 3969 4536 4704 5292 6048 7056 7938 9072 10584 14112 15876 18144 21168 31752 42336 63504 127008

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