Number of the day: 16634598676

Andrey Andreyevich Markov was born on this day 161 years ago.

Properties of the number 16634598676:

16634598676 = 2² × 37 × 43 × 97 × 26947 is composite and not squarefree.
16634598676 has 5 distinct prime factors, 48 divisors, 79 antidivisors and 7822531584 totatives.
16634598676 has a prime digit sum 61 in base 10.
Reversing the decimal digits of 16634598676 results in a prime.
16634598676 = (14919 × 14920)/2 + … + (15066 × 15067)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
16634598676 = 4158649670² - 4158649668² = 112395974² - 112395900² = 96712826² - 96712740² = 42872774² - 42872580² = 2615450² - 2612268² = 1162310² - 1155132² = 1001210² - 992868² = 181274² - 127380² is the difference of 2 nonnegative squares in 8 ways.
16634598676 is the difference of 2 positive pentagonal numbers in 8 ways.
16634598676 = 626² + 2364² + 128952² is the sum of 3 positive squares.
16634598676² = 11146896020² + 12347330976² = 8064698160² + 14548900876² = 6539821324² + 15295117200² = 5395004976² + 15735431180² is the sum of 2 positive squares in 4 ways.
16634598676² is the sum of 3 positive squares.
16634598676 is a proper divisor of 1543⁵⁰⁴ - 1.
16634598676 = '1663459867' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 172614

John Forbes Nash, Jr. was born on this day 89 years ago.

Properties of the number 172614:

172614 = 2 × 3 × 13 × 2213 is the 156892^th composite number and is squarefree.
172614 has 4 distinct prime factors, 16 divisors, 7 antidivisors and 53088 totatives.
172614 has a semiprime digit sum 21 in base 10.
172614 has a Fibonacci digit sum 21 in base 10.
172614 has a triangular digit sum 21 in base 10.
172614 is the sum of 2 positive triangular numbers.
172614 is the difference of 2 positive pentagonal numbers in 4 ways.
172614 = 10² + 17² + 415² is the sum of 3 positive squares.
172614² = 79686² + 153120² = 66390² + 159336² = 52614² + 164400² = 14664² + 171990² is the sum of 2 positive squares in 4 ways.
172614² is the sum of 3 positive squares.
172614 is a proper divisor of 1093¹⁴ - 1.
172614 = '1726' + '14' is the concatenation of 2 semiprime numbers.

Number of the day: 73084

Vladimir Igorevich Arnold was born on this day 80 years ago.

Properties of the number 73084:

73084 = 2² × 11² × 151 is the 65856^th composite number and is not squarefree.
73084 has 3 distinct prime factors, 18 divisors, 25 antidivisors and 33000 totatives.
73084 has a semiprime digit sum 22 in base 10.
73084 = 18272² - 18270² = 1672² - 1650² = 272² - 30² is the difference of 2 nonnegative squares in 3 ways.
73084 is the sum of 2 positive triangular numbers.
73084 is the difference of 2 positive pentagonal numbers in 4 ways.
73084 is not the sum of 3 positive squares.
73084² is the sum of 3 positive squares.
73084 is a proper divisor of 1693⁶ - 1.
73084 is palindromic in (at least) base -12.
73084 in base 45 = a44 and consists of only the digits '4' and 'a'.

Number of the day: 21429

Properties of the number 21429:

21429 = 3² × 2381 is the 19023^th composite number and is not squarefree.
21429 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 14280 totatives.
21429 has a Fibonacci digit product 144 in base 10.
21429 = 1³ + 21³ + 23³ is the sum of 3 positive cubes in 1 way.
21429 = 10715² - 10714² = 3573² - 3570² = 1195² - 1186² is the difference of 2 nonnegative squares in 3 ways.
21429 is the sum of 2 positive triangular numbers.
21429 is the difference of 2 positive pentagonal numbers in 1 way.
21429 = 102² + 105² is the sum of 2 positive squares in 1 way.
21429 = 7² + 8² + 146² is the sum of 3 positive squares.
21429² = 621² + 21420² is the sum of 2 positive squares in 1 way.
21429² is the sum of 3 positive squares.
21429 is a proper divisor of 1021²¹ - 1.
21429 = '2' + '1429' is the concatenation of 2 prime numbers.
21429 is palindromic in (at least) the following bases: -32, and -51.
21429 in base 11 = 15111 and consists of only the digits '1' and '5'.
21429 in base 28 = r99 and consists of only the digits '9' and 'r'.
21429 in base 34 = ii9 and consists of only the digits '9' and 'i'.
21429 in base 35 = hh9 and consists of only the digits '9' and 'h'.

The number 21429 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031846: Period of continued fraction for sqrt(n) contains exactly 78 ones.
A037101: Trajectory of 3 under map n->7n+1 if n odd, n->n/2 if n even
A271412: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 358", based on the 5-celled von Neumann neighborhood.
A271623: a(0)=7; a(n) = 7*a(n-1) + 1 if a(n-1) is odd, a(n) = a(n-1)/2 otherwise.

Number of the day: 2716

Properties of the number 2716:

2716 = 2² × 7 × 97 is the 2319^th composite number and is not squarefree.
2716 has 3 distinct prime factors, 12 divisors, 5 antidivisors and 1152 totatives.
2716 = 17³ - 13³ is the difference of 2 positive cubes in 1 way.
2716 = (15 × 16)/2 + … + (26 × 27)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
2716 = 680² - 678² = 104² - 90² is the difference of 2 nonnegative squares in 2 ways.
2716 is the sum of 2 positive triangular numbers.
2716 is the difference of 2 positive pentagonal numbers in 2 ways.
2716 is not the sum of 3 positive squares.
2716² = 1820² + 2016² is the sum of 2 positive squares in 1 way.
2716² is the sum of 3 positive squares.
2716 is a proper divisor of 1163² - 1.
2716 is palindromic in (at least) the following bases: 24, 96, -21, and -46.
2716 in base 15 = c11 and consists of only the digits '1' and 'c'.
2716 in base 24 = 4h4 and consists of only the digits '4' and 'h'.

The number 2716 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002895: Domb numbers: number of 2n-step polygons on diamond lattice.
A007655: Standard deviation of A007654.
A063490: (2*n-1)*(7*n^2-7*n+6)/6.
A075232: Numbers n such that n^9 is an interprime = average of two successive primes.
A076454: Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly one way.
A144138: Chebyshev polynomial of the second kind U(3,n).
A180281: Triangle read by rows: T(n,k) = number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to k.
A181061: a(n) is the smallest positive number such that the decimal digits of n*a(n) are all 0, 1 or 2.
A196636: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4
A245397: A(n,k) is the sum of k-th powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Number of the day: 1906

John Edensor Littlewood was born on this day 132 years ago.

Properties of the number 1906:

1906 = 2 × 953 is semiprime and squarefree.
1906 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 952 totatives.
1906 has sum of divisors equal to 2862 which is an oblong number.
Reversing the decimal digits of 1906 results in a prime.
1906 is the sum of 2 positive triangular numbers.
1906 is the difference of 2 positive pentagonal numbers in 2 ways.
1906 = 15² + 41² is the sum of 2 positive squares in 1 way.
1906 = 13² + 21² + 36² is the sum of 3 positive squares.
1906² = 1230² + 1456² is the sum of 2 positive squares in 1 way.
1906² is the sum of 3 positive squares.
1906 is a proper divisor of 431⁷ - 1.
1906 = '190' + '6' is the concatenation of 2 triangular numbers.
1906 is an emirpimes in (at least) the following bases: 3, 5, 7, 11, 13, 18, 21, 23, 25, 29, 31, 32, 33, 35, 38, 46, 47, 48, 49, 51, 54, 56, 59, 67, 70, 71, 72, 74, 76, 81, 83, 84, 86, 89, 90, 91, 96, and 98.
1906 is palindromic in (at least) the following bases: 28, -19, and -34.
1906 in base 3 = 2121121 and consists of only the digits '1' and '2'.
1906 in base 16 = 772 and consists of only the digits '2' and '7'.
1906 in base 19 = 556 and consists of only the digits '5' and '6'.
1906 in base 27 = 2gg and consists of only the digits '2' and 'g'.
1906 in base 28 = 2c2 and consists of only the digits '2' and 'c'.
1906 in base 43 = 11E and consists of only the digits '1' and 'E'.

The number 1906 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006315: Numbers n such that n^32 + 1 is prime.
A077065: Semiprimes of form prime - 1.
A090495: Numbers n such that numerator(Bernoulli(2*n)/(2*n)) is different from numerator(Bernoulli(2*n)/(2*n*(2*n-1))).
A098185: If f(x) = (sum of unitary proper divisors of x) = A063919(x) is iterated, the iteration may lead to a fixed point which is either equals 0 or it is from A002827, a unitary perfect number > 1: 6,60,90,87360... Here initial values are collected for which the iteration ends in a unitary perfect number > 1.
A120186: a(n)=ceiling( sum_{i=1..n-1} a(i)/7), a(1)=1.
A206128: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors
A217135: Numbers n such that 3^n - 8 is prime.
A229717: T(n,k)=Number of arrays of length n that are sums of k consecutive elements of length n+k-1 permutations of 0..n+k-2, and no two consecutive rises or falls in the latter permutation
A238340: Number of partitions of 4n into 4 parts.
A281205: T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

Number of the day: 21414

Properties of the number 21414:

21414 = 2 × 3 × 43 × 83 is the 19009^th composite number and is squarefree.
21414 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 6888 totatives.
21414 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 21414 results in an oblong number.
21414 is the difference of 2 positive pentagonal numbers in 2 ways.
21414 = 10² + 17² + 145² is the sum of 3 positive squares.
21414² is the sum of 3 positive squares.
21414 is a proper divisor of 1327⁶ - 1.
21414 = '214' + '14' is the concatenation of 2 semiprime numbers.
21414 is palindromic in (at least) the following bases: 41, -30, and -40.
21414 in base 9 = 32333 and consists of only the digits '2' and '3'.
21414 in base 13 = 9993 and consists of only the digits '3' and '9'.
21414 in base 30 = nno and consists of only the digits 'n' and 'o'.
21414 in base 39 = E33 and consists of only the digits '3' and 'E'.
21414 in base 41 = CUC and consists of only the digits 'C' and 'U'.

The number 21414 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032240: Number of identity bracelets of n beads of 3 colors.
A043468: Numbers n such that number of 3's in base 9 is 4.
A074303: Sum of squares of digits of n is equal to the largest prime factor of n reversed, where the largest prime factor is not a palindrome.
A167690: The even composites n such that n=q*g*j*y and q+g=j*y where q,g,j,y are primes.
A200075: G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1 + x^2*A(x)^3).
A211850: Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1
A260761: Number of (n+2)X(2+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010011
A283003: Intersection of A003052 and A283002.