• 105414² = 11112111396 is the smallest square that contains exactly seven digits '1'.

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105414 has 8 divisors (see below), whose sum is σ = 210840. Its totient is φ = 35136.

The previous prime is 105407. The next prime is 105437. The reversal of 105414 is 414501.

It is a sphenic number, since it is the product of 3 distinct primes.

105414 is an admirable number.

It is a super-2 number, since 2×105414² = 22224222792, which contains 22 as substring.

It is an alternating number because its digits alternate between odd and even.

It is a nialpdrome in base 11.

It is a junction number, because it is equal to n+sod(n) for n = 105393 and 105402.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 8779 + ... + 8790.

It is an arithmetic number, because the mean of its divisors is an integer number (26355).

2¹⁰⁵⁴¹⁴ is an apocalyptic number.

105414 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

105414 is a wasteful number, since it uses less digits than its factorization.

105414 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17574.

The product of its (nonzero) digits is 80, while the sum is 15.

The square root of 105414 is about 324.6752223376. The cubic root of 105414 is about 47.2388624683.

Adding to 105414 its reverse (414501), we get a palindrome (519915).

The spelling of 105414 in words is "one hundred five thousand, four hundred fourteen".