• 61 can be written using four 4's:

• If ^{3} + 3 and (+1)^{3} + 3 are both divisible by a number > 1, then = 61. (For example, this happens for = 56.)

61 has 2 divisors, whose sum is σ = 62. Its totient is φ = 60.

The previous prime is 59. The next prime is 67. The reversal of 61 is 16.

61 is nontrivially palindromic in base 6.

61 is an esthetic number in base 9, base 11 and base 14, because in such bases its adjacent digits differ by 1.

It is a m-pointer prime, because the next prime (67) can be obtained adding 61 to its product of digits (6).

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 36 + 25 = 6^2 + 5^2 .

It is a cyclic number.

It is not a de Polignac number, because 61 - 2^{1} = 59 is a prime.

Together with 59, it forms a pair of twin primes.

61 is a repfigit number.

It is a fibodiv number, since the Fibonacci-like sequence with seeds 6 and 1 contains 61 itself.

It is a magnanimous number.

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

61 is an undulating number in base 6.

It is a plaindrome in base 7, base 9, base 11, base 13, base 14 and base 16.

It is a nialpdrome in base 4, base 5, base 8, base 10, base 12 and base 15.

It is a congruent number.

It is a panconsummate 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 as a sum of consecutive naturals, namely, 30 + 31.

It is an arithmetic number, because the mean of its divisors is an integer number (31).

61 is the 6-th centered square number, the 5-th hex number and also the 4-th centered decagonal number.

It is an amenable number.

61 is a deficient number, since it is larger than the sum of its proper divisors (1).

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

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

The product of its digits is 6, while the sum is 7.

The square root of 61 is about 7.8102496759. The cubic root of 61 is about 3.9364971831.

Adding to 61 its reverse (16), we get a palindrome (77).

Subtracting from 61 its reverse (16), we obtain a triangular number (45 = T_{9}).

The spelling of 61 in words is "sixty-one", and thus it is an aban number and an uban number.

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