• 65 can be written using four 4's:

65 has 4 divisors (see below), whose sum is σ = 84. Its totient is φ = 48.

The previous prime is 61. The next prime is 67. The reversal of 65 is 56.

Added to its reverse (56) it gives a square (121 = 11^{2}).

65 is nontrivially palindromic in base 2, base 4, base 8 and base 12.

It is a Cunningham number, because it is equal to 2^{6}+1.

65 is an esthetic number in base 8, base 10 and base 15, because in such bases its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 16 + 49 = 4^2 + 7^2 .

It is a sliding number, since 65 = 25 + 40 and 1/25 + 1/40 = 0.065.

It is a cyclic number.

It is a Cullen number, since it is equal to 4×2^{4}+1.

65 is a rare number.

It is not a de Polignac number, because 65 - 2^{2} = 61 is a prime.

It is a magnanimous number.

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

It is a Duffinian number.

65 is an undulating number in base 8.

It is a Curzon number.

65 is a nontrivial repdigit in base 12.

It is a plaindrome in base 6, base 7, base 11, base 12, base 14 and base 15.

It is a nialpdrome in base 9, base 10, base 12, base 13 and base 16.

It is a zygodrome in base 12.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 65.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2 + ... + 11.

It is an arithmetic number, because the mean of its divisors is an integer number (21).

It is the magic constant of a 5 × 5 magic square.

It is a Proth number, since it is equal to 1 ⋅ 2^{6} + 1 and 1 < 2^{6}.

65 is the 5-th octagonal number.

It is an amenable number.

65 is a deficient number, since it is larger than the sum of its proper divisors (19).

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

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

The sum of its prime factors is 18.

The product of its digits is 30, while the sum is 11.

The square root of 65 is about 8.0622577483. The cubic root of 65 is about 4.0207257586.

Adding to 65 its reverse (56), we get a palindrome (121).

The spelling of 65 in words is "sixty-five", and thus it is an aban number, an oban number, and an uban number.

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