## Kurt GĂ¶del was born on this day 110 years ago.

### Properties of the number 1718:

1718 = 2 × 859 is semiprime and squarefree.1718 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 858 totatives.

1718 has an emirp digit sum 17 in base 10.

1718 has an oblong digit product 56 in base 10.

Reversing the decimal digits of 1718 results in a prime.

1718 = 1

^{2}+ 6

^{2}+ 41

^{2}is the sum of 3 positive squares.

1718

^{2}is the sum of 3 positive squares.

1718 is a divisor of 599

^{6}- 1.

1718 is an emirpimes in (at least) the following bases: 4, 5, 9, 15, 17, 19, 25, 31, 34, 35, 36, 37, 38, 39, 40, 45, 50, 53, 54, 55, 58, 64, 66, 67, 71, 72, 74, 76, 78, 79, 83, 87, 92, 94, 95, 99, and 100.

1718 is palindromic in (at least) the following bases: 16, and 26.

1718 in base 5 = 23333 and consists of only the digits '2' and '3'.

1718 in base 12 = bb2 and consists of only the digits '2' and 'b'.

1718 in base 13 = a22 and consists of only the digits '2' and 'a'.

1718 in base 14 = 8aa and consists of only the digits '8' and 'a'.

1718 in base 16 = 6b6 and consists of only the digits '6' and 'b'.

1718 in base 18 = 558 and consists of only the digits '5' and '8'.

1718 in base 25 = 2ii and consists of only the digits '2' and 'i'.

1718 in base 26 = 2e2 and consists of only the digits '2' and 'e'.

### The number 1718 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A000954: Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.

A001704: a(n) = concatenation {n,n+1}.

A056045: a(n) = Sum_{k|n} binomial(n,k).

A071148: Partial sums of sequence of odd primes [A065091]; a(n) = sum of the first n odd primes.

A077295: Partition the concatenation 1234567...of natural numbers into successive strings which are even, all different and > 2. (0's never taken as the most significant digit.)

A112816: Numbers n such that 9*LCM(1,2,3,...,n) equals the denominator of the n-th harmonic number H(n).

A159051: Numbers n such that Fibonacci(n-2) is divisible by n.

A160164: Number of toothpicks after n-th stage in the I-toothpick structure of A139250.

A183561: Number of partitions of n containing a clique of size 4.

A187705: T(n,k)=Number of (n+1)X(n+1) 0..k arrays with each 2X2 subblock off diagonal and antidiagonal nonsingular and the array of 2X2 subblock determinants antisymmetric about the diagonal and antidiagonal

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