Number of the day: 9935

Properties of the number 9935:

9935 = 5 × 1987 is semiprime and squarefree.
9935 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7944 totatives.
9935 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 9935 results in a prime.
9935 = 4968² - 4967² = 996² - 991² is the difference of 2 nonnegative squares in 2 ways.
9935 is the difference of 2 positive pentagonal numbers in 2 ways.
9935 is not the sum of 3 positive squares.
9935² = 5961² + 7948² is the sum of 2 positive squares in 1 way.
9935² is the sum of 3 positive squares.
9935 is a divisor of 647¹² - 1.
9935 is an emirpimes in (at least) the following bases: 2, 3, 5, 6, 11, 19, 21, 23, 24, 27, 30, 33, 35, 36, 37, 40, 44, 49, 59, 62, 67, 77, 79, 80, 84, 89, 92, and 100.
9935 is palindromic in (at least) the following bases: 52, and -77.
9935 in base 3 = 111121222 and consists of only the digits '1' and '2'.
9935 in base 31 = aaf and consists of only the digits 'a' and 'f'.
9935 in base 44 = 55Z and consists of only the digits '5' and 'Z'.
9935 in base 51 = 3ff and consists of only the digits '3' and 'f'.
9935 in base 52 = 3Z3 and consists of only the digits '3' and 'Z'.
9935 in base 57 = 33H and consists of only the digits '3' and 'H'.

The number 9935 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A147357: Number of n X n binary arrays symmetric about both diagonal and antidiagonal with all ones connected only in a 0110-0110-1111 pattern in any orientation.
A148616: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 0, 0), (1, 1, -1)}
A239852: Number of nX2 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4

Number of the day: 82801610348001

Properties of the number 82801610348001:

82801610348001 = 3 × 47 × 443 × 1325610527 is composite and squarefree.
82801610348001 has 4 distinct prime factors, 16 divisors, 43 antidivisors and 53904626429264 totatives.
82801610348001 has a sphenic digit sum 42 in base 10.
82801610348001 has an oblong digit sum 42 in base 10.
82801610348001 = 41400805174001² - 41400805174000² = 13800268391335² - 13800268391332² = 880868195215² - 880868195168² = 293622731801² - 293622731660² = 93455542375² - 93455541932² = 31151848049² - 31151846720² = 1988426201² - 1988405380² = 662836495² - 662774032² is the difference of 2 nonnegative squares in 8 ways.
82801610348001 is the sum of 2 positive triangular numbers.
82801610348001 is the difference of 2 positive pentagonal numbers in 4 ways.
82801610348001 = 1759² + 11164² + 9099532² is the sum of 3 positive squares.
82801610348001² is the sum of 3 positive squares.
82801610348001 is a divisor of 1787^22535378942 - 1.
82801610348001 = '828016103' + '48001' is the concatenation of 2 semiprime numbers.

Number of the day: 460219

Properties of the number 460219:

460219 = 89 × 5171 is semiprime and squarefree.
460219 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 454960 totatives.
460219 has a semiprime digit sum 22 in base 10.
460219 = 230110² - 230109² = 2630² - 2541² is the difference of 2 nonnegative squares in 2 ways.
460219 is the sum of 2 positive triangular numbers.
460219 is the difference of 2 positive pentagonal numbers in 2 ways.
460219 = 25² + 63² + 675² is the sum of 3 positive squares.
460219² = 201669² + 413680² is the sum of 2 positive squares in 1 way.
460219² is the sum of 3 positive squares.
460219 is a divisor of 1303²² - 1.
460219 is an emirpimes in (at least) the following bases: 4, 5, 8, 9, 11, 12, 13, 17, 19, 21, 23, 24, 25, 31, 34, 35, 43, 46, 47, 50, 56, 59, 60, 62, 64, 65, 67, 72, 74, 76, 78, 79, 81, 88, 92, 94, 96, 97, and 98.
460219 is palindromic in (at least) base -83.

Number of the day: 136868196

Properties of the number 136868196:

136868196 = 2² × 3 × 709 × 16087 is the 129123028^th composite number and is not squarefree.
136868196 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 45555552 totatives.
136868196 = 34217050² - 34217048² = 11405686² - 11405680² = 48970² - 47552² = 18214² - 13960² is the difference of 2 nonnegative squares in 4 ways.
136868196 is the sum of 2 positive triangular numbers.
136868196 is the difference of 2 positive pentagonal numbers in 2 ways.
136868196 = 46² + 404² + 11692² is the sum of 3 positive squares.
136868196² = 49998396² + 127409040² is the sum of 2 positive squares in 1 way.
136868196² is the sum of 3 positive squares.
136868196 is a divisor of 1409²⁴⁷⁸ - 1.

Number of the day: 20565182705512

Properties of the number 20565182705512:

20565182705512 = 2³ × 17 × 109 × 307 × 4518859 is composite and not squarefree.
20565182705512 has 5 distinct prime factors, 64 divisors, 147 antidivisors and 9557710027776 totatives.
20565182705512 has an emirpimes digit sum 49 in base 10.
20565182705512 is the difference of 2 nonnegative squares in 16 ways.
20565182705512 is the sum of 2 positive triangular numbers.
20565182705512 is the difference of 2 positive pentagonal numbers in 8 ways.
20565182705512 = 966² + 13120² + 4534866² is the sum of 3 positive squares.
20565182705512² = 9822011168040² + 18068061222112² = 9677733037888² + 18145749446040² = 1908910645088² + 20476396163880² = 11320284058080² + 17169097488088² is the sum of 2 positive squares in 4 ways.
20565182705512² is the sum of 3 positive squares.
20565182705512 is a divisor of 613^9037716 - 1.
20565182705512 = '2056518270551' + '2' is the concatenation of 2 prime numbers.

Number of the day: 660647

George Boole was born on this day 201 years ago.

Properties of the number 660647:

660647 = 13 × 89 × 571 is a sphenic number and squarefree.
660647 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 601920 totatives.
660647 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 660647 results in a sphenic number.
660647 = 330324² - 330323² = 25416² - 25403² = 3756² - 3667² = 864² - 293² is the difference of 2 nonnegative squares in 4 ways.
660647 is the sum of 2 positive triangular numbers.
660647 is the difference of 2 positive pentagonal numbers in 3 ways.
660647 is not the sum of 3 positive squares.
660647² = 289497² + 593840² = 38828² + 659505² = 436815² + 495628² = 254095² + 609828² is the sum of 2 positive squares in 4 ways.
660647² is the sum of 3 positive squares.
660647 is a divisor of 109¹³² - 1.
660647 is palindromic in (at least) base 96.
660647 in base 34 = grgr and consists of only the digits 'g' and 'r'.

Number of the day: 5080

Properties of the number 5080:

5080 = 2³ × 5 × 127 is the 4401^th composite number and is not squarefree.
5080 has 3 distinct prime factors, 16 divisors, 7 antidivisors and 2016 totatives.
5080 has an emirp digit sum 13 in base 10.
5080 has a Fibonacci digit sum 13 in base 10.
5080 = 1271² - 1269² = 637² - 633² = 259² - 249² = 137² - 117² is the difference of 2 nonnegative squares in 4 ways.
5080 is the difference of 2 positive pentagonal numbers in 2 ways.
5080 = 18² + 20² + 66² is the sum of 3 positive squares.
5080² = 3048² + 4064² is the sum of 2 positive squares in 1 way.
5080² is the sum of 3 positive squares.
5080 is a divisor of 509² - 1.
5080 is palindromic in (at least) the following bases: -35, and -36.
5080 in base 22 = aak and consists of only the digits 'a' and 'k'.
5080 in base 35 = 455 and consists of only the digits '4' and '5'.

The number 5080 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A086417: Sum of divisors of 3-smooth numbers.
A100155: Structured truncated octahedral numbers.
A104494: Positive integers n such that n^17 + 1 is semiprime (A001358).
A173723: Number of symmetry classes of 3x3 semimagic squares with distinct positive values < n.
A175926: Sum of divisors of cubes.
A177011: Define two triangular arrays by: B(0,0)=C(0,0)=1, B(0,r)=C(0,r)=0 for r>0, C(t,-1)=C(t,0); and for t,r >= 0, B(t+1,r)=C(t,r-1)+2C(t,r)-B(t,r), C(t+1,r)=B(t+1,r)+2B(t+1,r+1)-C(t,r). Sequence gives array B(t,r) read by rows.
A189449: T(n,k)=Number of nXk array permutations with each element moving zero or one space horizontally or diagonally
A239056: Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1.
A256708: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 8 as largest digit.
A264643: T(n,k)=Number of nXk arrays of permutations of 0..n*k-1 with rows nondecreasing modulo 3 and columns nondecreasing modulo 4.