102114 has 32 divisors (see below), whose sum is σ = 238080. Its totient is φ = 32400.

The previous prime is 102107. The next prime is 102121. The reversal of 102114 is 411201.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (102107) and next prime (102121).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 102096 and 102105.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 102114.

It is an unprimeable number.

102114 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1644 + ... + 1704.

It is an arithmetic number, because the mean of its divisors is an integer number (7440).

2^{102114} is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 102114, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119040).

102114 is an abundant number, since it is smaller than the sum of its proper divisors (135966).

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

102114 is a wasteful number, since it uses less digits than its factorization.

102114 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 103 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 9.

The square root of 102114 is about 319.5528125365. The cubic root of 102114 is about 46.7406875176.

Adding to 102114 its reverse (411201), we get a palindrome (513315).

It can be divided in two parts, 1021 and 14, that added together give a triangular number (1035 = T_{45}).

The spelling of 102114 in words is "one hundred two thousand, one hundred fourteen", and thus it is an iban number.

Divisors: 1 2 3 6 9 18 27 31 54 61 62 93 122 183 186 279 366 549 558 837 1098 1647 1674 1891 3294 3782 5673 11346 17019 34038 51057 102114

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