Today is the 17^{th} day of the
month. The properties of 17 include:
17 is a prime number. It is a Chen, emirp, good, hungry, Pierpont,
and strong prime. It is the smaller
prime in a twin prime pair, and the larger prime in a cousin prime pair.
17 is an amenable, arithmetic, cyclic, deficient,
evil, hungry, odd, pernicious, polite, Proth, and Woodall number.
It has 2 divisors, whose sum is σ = 18.
Its totient is φ = 16. The product of
its digits is 7, while the sum is 8.
17 can be expressed as the sum of two
squares: 17 = 1^2 + 4^2. It can also
be express as the sum of two fourth powers: 17 = 1^4 + 2^4 (it is the
smallest integer to have this property). 17 can also be expressed as the difference of two
squares: 17 = 9^2 – 8^2.
17 is the hypotenuse of a Pythagorean
triangle: 17^2 = 15^1 + 8^2.
It can be written as a sum of positive
squares in only one way, i.e., 17 = 16 + 1 = 4^2 + 1^2.
17 is nontrivially palindromic in base 2,
and base 4.
17 is an esthetic number in base 4, base
5, base 7, base 8 and base 15, because in such bases it adjacent digits
differ by 1.
It is a Leyland number of the form 3^2 +
2^3.
17 is a palindromic number when written
in base 2, base 4, and base 16. 17 is
an undulating number when written in base 4.
It is the 10th Perrin number.
It is a plaindrome in base 3, base 6,
base 7, base 9, base 10, base 11, base 12, base 13, base 14, base 15 and base
16. It is a nialpdrome in base 5, base
8 and base 16. It is a zygodrome in
base 16.
A polygon with 17 sides can be
constructed with ruler and compass.
17 is an equidigital number, since it
uses as much as digits as its factorization.
There are 17 distinct sets of regular
polygons that can be packed around a point (e.g., 4 squares, 2 hexagons and 2
triangles, etc.).
There are exactly 17 ways to express 17
as the sum of 1 or more primes  17 is the only integer which is equal to the
number of prime partitions of itself.
17 is the number of wallpaper groups.
17 is the only prime of the form p^q + q^p,
where p and q are prime.
17 is the only multidigit number n such
that n + SOD(n) and n  SOD(n) are square numbers, where SOD means sum of
digits.
17 is the number of syllables in a haiku.
17 is the smallest odd prime such that no
odd Fibonacci number is divisible by it.
17 is the minimum number of Sudoku clues
that produces a unique answer.

Today is the 168^{th} day of the
year. Properties of 168 include:
168 is a 57gonal, abundant, amenable,
arithmetic, composite, even, odious, pernicious, polite, practical, wasteful and
Zumkeller number.
168 is the number of hours in a week.
168 is the number of primes less than
1000.
168 is the total number of spots on a set
of dominoes.
168 can be expressed as the sum of three
squares: 168 = 2^2+8^2+10^2. 168 can
be expressed as the difference of two squares in three different ways: 168 =
17^2 – 11^2 = 23^2 – 19^2 = 43^2 – 41^2
It has 16 divisors, whose sum is σ = 480.
Its totient is φ = 48. The sum of its
prime factors is 16 (or 12 counting only the distinct ones). The product of its digits is 48, while the
sum is 15.
It is the short leg of a Pythagorean
triple: 168^2 + 3526^2 = 3530^2.
168 is nontrivially palindromic and
repdigit number when written in base 13, base 20, base 24, and base 27.
It is a nude number because it is
divisible by every one of its digits.
168 is an idoneal number.
It is one of the 548 LynchBell numbers.
It is a plaindrome in base 5, base 10 and
base 13. It is a nialpdrome in base 4,
base 6, base 7, base 13, base 14, base 15 and base 16. It is a zygodrome in base 5 and base 13.
It is a pseudoperfect number, because it
is the sum of a subset of its proper divisors.

Today is the 1629^{th} day of the
decade. The properties of 1629 include:
1629 is a 47gonal, 544gonal, amenable,
apocalyptic, composite, congruent, deficient, Curzon, Duffian, odd, odious,
pernicious, polite, and wasteful number.
It has 6 divisors, whose sum is σ = 2366.
Its totient is φ = 1080. The sum of
its prime factors is 187 (or 184 counting only the distinct ones). The product of its digits is 108, while the
sum is 18.
It can be written as a sum of positive
squares in only one way, i.e., 1629 = 900 + 729 = 30^2 + 27^2. It can also be written as the difference of
two squares in three different ways: 1629 = 95^2 – 86^2 = 273^2 – 270^2 = 815^2
– 814^2.
It is the short leg of a Pythagorean
triple: 1629^2 + 147420^2 = 147429^2.
It is a nialpdrome in base 9 and base 13.

Today is the 5281^{st} day of the
century. The properties of 5281 include:
5281 is a prime number. It is a weak prime, and an apointer
prime. It is the larger of a pair of
twin primes.
It is an amenable, arithmetic, centered
decagonal, concentric 22gonal, cyclic, deficient, happy, odd, odious,
pernicious, polite and squarefree number.
It has 2 divisors, whose sum is σ = 5282.
Its totient is φ = 5280. The product
of its digits is 80, while the sum is 16.
It can be written as a sum of positive
squares in only one way: 5881 = 3600 + 1681 = 60^2 + 41^2 . It can also be written as the difference of
two squares: 5281 = 2641^2 – 2640^2.
It is short leg of a Pythagorean triple: 5281^2
+ 13944480^2 = 13944481^2. It is also
the hypotenuse of a different Pythagorean triple: 5281^2 = 1919^2+4920^2.

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