Number of the day: 4361400865

Properties of the number 4361400865:

4361400865 is a cyclic number.
4361400865 = 5 × 5419 × 160967 is a sphenic number and squarefree.
4361400865 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 3488455152 totatives.
4361400865 has an emirp digit sum 37 in base 10.
4361400865 = 809³ + 1114³ + 1348³ is the sum of 3 positive cubes in 1 way.
4361400865 = 2180700433² - 2180700432² = 436140089² - 436140084² = 405127² - 399708² = 94031² - 66936² is the difference of 2 nonnegative squares in 4 ways.
4361400865 is the difference of 2 positive pentagonal numbers in 3 ways.
4361400865 = 1025² + 2436² + 65988² is the sum of 3 positive squares.
4361400865² = 2616840519² + 3489120692² is the sum of 2 positive squares in 1 way.
4361400865² is the sum of 3 positive squares.
4361400865 is a proper divisor of 127²³⁵⁵⁶ - 1.

Number of the day: 36779

Properties of the number 36779:

36779 is a cyclic number.
36779 and 36781 form a twin prime pair.
36779 has 13 antidivisors and 36778 totatives.
Reversing the decimal digits of 36779 results in a semiprime.
36779 = 18390² - 18389² is the difference of 2 nonnegative squares in 1 way.
36779 is the difference of 2 positive pentagonal numbers in 1 way.
36779 = 3² + 17² + 191² is the sum of 3 positive squares.
36779² is the sum of 3 positive squares.
36779 is a proper divisor of 1879³⁷ - 1.
36779 = '3' + '6779' is the concatenation of 2 prime numbers.
36779 is an emirp in (at least) the following bases: 7, 9, 11, 13, 14, 19, 29, 31, 37, 43, 46, 49, 51, 57, 59, 69, 73, 79, 84, 91, and 98.
36779 is palindromic in (at least) base 81.
36779 in base 46 = HHP and consists of only the digits 'H' and 'P'.
36779 in base 49 = FFT and consists of only the digits 'F' and 'T'.

The number 36779 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001606: Indices of prime Lucas numbers.
A078848: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[2,6,4]; short d-string notation of pattern = [264].
A078948: Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,2).
A126238: Primes of the form p = prime(n) = (prime(n+3)+prime(n-1))/2.
A130736: Primes n such that n+2, n*(n+2)+12 and n*(n+2)+14 are also prime.
A137476: Prime numbers p such that p^3 - (p+1)^2 and p^3 + (p+1)^2 are both primes.
A216576: Numbers n such that n-th Lucas number is prime, but cannot be written in the form a^2 + 10*b^2.
A226719: a(n) = the first member of a twin prime pair whose sum equals the sums of n consecutive pairs of twin primes.
A250025: Lesser of twin prime pairs of the form (40n - 21, 40n - 19).
A276848: For a lesser p of twin primes, let B_(p+2) and B_p be sequences defined as A159559, but with initial terms p+2 and p respectively. The sequence lists p for which all differences B_(p+2)(n)-B_p(n)<=6.

Number of the day: 29855568

Properties of the number 29855568:

29855568 = 2⁴ × 3 × 107 × 5813 is the 28006194^th composite number and is not squarefree.
29855568 has 4 distinct prime factors, 40 divisors, 19 antidivisors and 9857152 totatives.
29855568 is the difference of 2 nonnegative squares in 12 ways.
29855568 is the sum of 2 positive triangular numbers.
29855568 is the difference of 2 positive pentagonal numbers in 1 way.
29855568 = 4² + 16² + 5464² is the sum of 3 positive squares.
29855568² = 16496832² + 24883920² is the sum of 2 positive squares in 1 way.
29855568² is the sum of 3 positive squares.
29855568 is a proper divisor of 641²⁹⁰⁶ - 1.

Number of the day: 7105633254325

Properties of the number 7105633254325:

7105633254325 = 5² × 17 × 23 × 1789 × 406327 is composite and not squarefree.
7105633254325 has 5 distinct prime factors, 48 divisors, 75 antidivisors and 5114636651520 totatives.
7105633254325 has a semiprime digit sum 46 in base 10.
Reversing the decimal digits of 7105633254325 results in a semiprime.
7105633254325 is the difference of 2 nonnegative squares in 24 ways.
7105633254325 is the sum of 2 positive triangular numbers.
7105633254325 is the difference of 2 positive pentagonal numbers in 23 ways.
7105633254325 = 4620² + 10673² + 2665614² is the sum of 3 positive squares.
7105633254325² = 4722291761300² + 5309424118125² = 592178938165² + 7080914351280² = 1414164237720² + 6963487879915² = 3774805460236² + 6020038843923² = 3046761337773² + 6419288846564² = 3343827413800² + 6269676400875² = 1086743909485² + 7022037568980² = 3009444672420² + 6436867771565² = 4965583709493² + 5082617668976² = 1454564925003² + 6955161020704² = 2704920870635² + 6570648904680² = 1778452646300² + 6879471646125² = 3633566601363² + 6106326039316² = 4436505729120² + 5550445104715² = 218937520467² + 7102259521244² = 2809684161045² + 6526538045560² = 1668175498500² + 6907040933075² = 3535419939821² + 6163670156172² = 4524727447360² + 5478764958645² = 332522982701² + 7097848435332² = 4263379952595² + 5684506603460² = 1989577311211² + 6821407924152² is the sum of 2 positive squares in 22 ways.
7105633254325² is the sum of 3 positive squares.
7105633254325 is a proper divisor of 919^4063260 - 1.

Number of the day: 53430

Properties of the number 53430:

53430 = 2 × 3 × 5 × 13 × 137 is the 47981^th composite number and is squarefree.
53430 has 5 distinct prime factors, 32 divisors, 15 antidivisors and 13056 totatives.
53430 has an emirpimes digit sum 15 in base 10.
53430 has a triangular digit sum 15 in base 10.
53430 = 58² + … + 70² is the sum of at least 2 consecutive positive squares in 1 way.
53430 is the sum of 2 positive triangular numbers.
53430 is the difference of 2 positive pentagonal numbers in 2 ways.
53430 = 26² + 35² + 227² is the sum of 3 positive squares.
53430² = 34320² + 40950² = 15930² + 51000² = 24600² + 47430² = 17856² + 50358² = 2886² + 53352² = 23184² + 48138² = 12168² + 52026² = 8778² + 52704² = 31242² + 43344² = 32058² + 42744² = 13152² + 51786² = 27126² + 46032² = 20550² + 49320² is the sum of 2 positive squares in 13 ways.
53430² is the sum of 3 positive squares.
53430 is a proper divisor of 311⁴ - 1.
53430 = '534' + '30' is the concatenation of 2 sphenic numbers.
53430 in base 37 = 1212 and consists of only the digits '1' and '2'.

The number 53430 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024205: [ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 odd positive integers}.
A072289: One eighty-fourth the area of primitive Pythagorean triangles with (increasing) square hypotenuses (precisely those of A008846).
A077521: a(1) = 1, a(n) = smallest squarefree number which begins with n and is a multiple of the previous term.
A111696: a(n) = C(n,a)+C(n,b)+C(n,c)... where n = abc... are the decimal digits of n.
A123975: Number of Garden of Eden partitions of n in Bulgarian Solitaire.
A274062: Even numbers such that the sum of the odd divisors is a Fibonacci number F and the sum of the even divisors is 2F.

Number of the day: 876266

Properties of the number 876266:

876266 = 2 × 438133 is semiprime and squarefree.
876266 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 438132 totatives.
876266 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 876266 results in an emirpimes.
876266 = 115² + 929² is the sum of 2 positive squares in 1 way.
876266 = 59² + 116² + 927² is the sum of 3 positive squares.
876266² = 213670² + 849816² is the sum of 2 positive squares in 1 way.
876266² is the sum of 3 positive squares.
876266 is a proper divisor of 43¹²⁵⁹ - 1.
876266 = '8762' + '66' is the concatenation of 2 sphenic numbers.
876266 is an emirpimes in (at least) the following bases: 2, 4, 6, 7, 9, 10, 16, 20, 21, 24, 28, 30, 34, 39, 40, 41, 43, 48, 50, 53, 62, 64, 65, 66, 67, 72, 76, 77, 80, 82, 83, 85, 86, 88, 89, 91, 93, 97, 98, and 99.

Number of the day: 11232018

John Wallis was born on this day 402 years ago.

Happy Fibonacci Day!

Properties of the number 11232018:

11232018 = 2 × 3² × 7 × 97 × 919 is the 10491197^th composite number and is not squarefree.
11232018 has 5 distinct prime factors, 48 divisors, 31 antidivisors and 3172608 totatives.
11232018 is the sum of 2 positive triangular numbers.
11232018 = 29² + 124² + 3349² is the sum of 3 positive squares.
11232018² = 7526610² + 8337168² is the sum of 2 positive squares in 1 way.
11232018² is the sum of 3 positive squares.
11232018 is a proper divisor of 971⁶ - 1.

Number of the day: 419339

Properties of the number 419339:

419339 = 17² × 1451 is the 384000^th composite number and is not squarefree.
419339 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 394400 totatives.
419339 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 419339 results in a semiprime.
419339 = 209670² - 209669² = 12342² - 12325² = 870² - 581² is the difference of 2 nonnegative squares in 3 ways.
419339 is the difference of 2 positive pentagonal numbers in 2 ways.
419339 = 17² + 55² + 645² is the sum of 3 positive squares.
419339² = 233611² + 348240² = 197336² + 370005² is the sum of 2 positive squares in 2 ways.
419339² is the sum of 3 positive squares.
419339 is a proper divisor of 1021⁸⁵ - 1.
419339 = '4' + '19339' is the concatenation of 2 semiprime numbers.

Number of the day: 7570

Properties of the number 7570:

7570 = 2 × 5 × 757 is a sphenic number and squarefree.
7570 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 3024 totatives.
7570 has a prime digit sum 19 in base 10.
7570 is the difference of 2 positive pentagonal numbers in 2 ways.
7570 = 53² + 69² = 1² + 87² is the sum of 2 positive squares in 2 ways.
7570 = 15² + 28² + 81² is the sum of 3 positive squares.
7570² = 4542² + 6056² = 1952² + 7314² = 174² + 7568² = 4680² + 5950² is the sum of 2 positive squares in 4 ways.
7570² is the sum of 3 positive squares.
7570 is a proper divisor of 1427⁴ - 1.
7570 is palindromic in (at least) the following bases: 3, 27, 39, 47, 87, -28, -86, and -87.
7570 in base 3 = 101101101 and consists of only the digits '0' and '1'.
7570 in base 20 = iia and consists of only the digits 'a' and 'i'.
7570 in base 27 = aaa and consists of only the digit 'a'.
7570 in base 35 = 66a and consists of only the digits '6' and 'a'.
7570 in base 39 = 4c4 and consists of only the digits '4' and 'c'.
7570 in base 43 = 442 and consists of only the digits '2' and '4'.
7570 in base 46 = 3QQ and consists of only the digits '3' and 'Q'.
7570 in base 47 = 3K3 and consists of only the digits '3' and 'K'.
7570 in base 61 = 226 and consists of only the digits '2' and '6'.

The number 7570 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007107: Number of labeled 2-regular digraphs with n nodes.
A048885: Number of nonisomorphic orthogonal arrays OA(4n,4n-1,2,2).
A060879: Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.
A069894: Centered square numbers: a(n) = 4*n^2 + 4*n + 2.
A154360: a(n) = 250*n - 180.
A210766: Number of 8-hoops with n symbols and no a-rooted trees.
A252167: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 2 3 4 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 2 3 4 6 or 7
A264925: G.f.: 1 / Product_{n>=0} (1 - x^(n+5))^((n+1)*(n+2)*(n+3)*(n+4)/4!).
A284990: Triangle T(n,t) read by rows: the number of n X n {0,1} matrices with trace t where each row sum and each column sum is 3.
A299285: Coordination sequence for "tea" 3D uniform tiling.

Number of the day: 3207

Properties of the number 3207:

3207 = 3 × 1069 is semiprime and squarefree.
3207 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 2136 totatives.
3207 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3207 results in an emirpimes.
3207 = 1604² - 1603² = 536² - 533² is the difference of 2 nonnegative squares in 2 ways.
3207 is the sum of 2 positive triangular numbers.
3207 is the difference of 2 positive pentagonal numbers in 1 way.
3207 is not the sum of 3 positive squares.
3207² = 2193² + 2340² is the sum of 2 positive squares in 1 way.
3207² is the sum of 3 positive squares.
3207 is a proper divisor of 1889⁴ - 1.
3207 is an emirpimes in (at least) the following bases: 2, 5, 7, 9, 10, 11, 15, 36, 39, 42, 44, 46, 47, 48, 50, 58, 59, 60, 62, 63, 69, 73, 74, 75, 77, 89, 90, 96, and 99.
3207 is palindromic in (at least) the following bases: 17, and -36.
3207 in base 17 = b1b and consists of only the digits '1' and 'b'.
3207 in base 56 = 11F and consists of only the digits '1' and 'F'.

The number 3207 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014670: G.f.: (1+x)*(1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)).
A072475: Sum of next n composite numbers.
A124200: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43 is prime.
A137994: a(n) is the smallest integer > a(n-1) such that {Pi^a(n)} < {Pi^a(n-1)}, where {x} = x - floor(x), a(1)=1.
A207542: Number of solid standard Young tableaux with n cells.
A243577: Integers of the form 8k+7 that can be written as a sum of four distinct 'almost consecutive' squares.
A243580: Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 1, m + 3, m + 5, where m == 2 (mod 4).
A293403: Greatest integer k such that k/n^2 < (3 + sqrt(5))/2.
A293405: The integer k that minimizes |k/n^2 - tau^2|, where tau = (1+sqrt(5))/2 (golden ratio).
A298791: Partial sums of A298789.

Number of the day: 5023

August Ferdinand Möbius was born on this day 228 years ago.

Properties of the number 5023:

5023 is a cyclic number.
5021 and 5023 form a twin prime pair.
5023 has 17 antidivisors and 5022 totatives.
5023 has a semiprime digit sum 10 in base 10.
5023 has a triangular digit sum 10 in base 10.
Reversing the decimal digits of 5023 results in a semiprime.
5023 = 2512² - 2511² is the difference of 2 nonnegative squares in 1 way.
5023 is the difference of 2 positive pentagonal numbers in 1 way.
5023 is not the sum of 3 positive squares.
5023² is the sum of 3 positive squares.
5023 is a proper divisor of 953³ - 1.
5023 is an emirp in (at least) the following bases: 2, 7, 13, 14, 16, 17, 26, 33, 35, 40, 41, 49, 52, 55, 56, 59, 61, 64, 65, 66, 68, 70, 71, 74, 77, 79, 82, 85, 88, 89, 91, 94, and 95.
5023 is palindromic in (at least) the following bases: 23, 54, 62, -29, -81, and -93.
5023 in base 23 = 9b9 and consists of only the digits '9' and 'b'.
5023 in base 28 = 6bb and consists of only the digits '6' and 'b'.
5023 in base 53 = 1ff and consists of only the digits '1' and 'f'.
5023 in base 54 = 1d1 and consists of only the digits '1' and 'd'.
5023 in base 61 = 1LL and consists of only the digits '1' and 'L'.
5023 in base 62 = 1J1 and consists of only the digits '1' and 'J'.

The number 5023 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031934: Lower prime of a pair of consecutive primes having a difference of 16.
A045711: Primes with first digit 5.
A046257: a(1) = 7; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A074982: Primes for which the three closest primes are smaller.
A119617: Integers of the form c(n)/b(n) where c(n+1)=c(n)+(n+1)^4 with c(0)=1 and b(n+1)=b(n)+(n+1)^2 with b(0)=1.
A127578: Primes congruent to 31 mod 32.
A134153: a(n) = 15n^2 + 9n + 1.
A142005: Primes congruent to 1 mod 31.
A153377: Larger of two consecutive prime numbers such that p1*p2*d+d=average of twin prime pairs, d (delta)=p2-p1.
A297410: Where prime race among 11n+1, ..., 11n+10 changes leader.

Number of the day: 1356

Properties of the number 1356:

1356 = 2² × 3 × 113 is the 1138^th composite number and is not squarefree.
1356 has 3 distinct prime factors, 12 divisors, 3 antidivisors and 448 totatives.
1356 has an emirpimes digit sum 15 in base 10.
1356 has a triangular digit sum 15 in base 10.
1356 has an oblong digit product 90 in base 10.
1356 has sum of divisors equal to 3192 which is an oblong number.
Reversing the decimal digits of 1356 results in a sphenic number.
1356 = 8² + … + 16² is the sum of at least 2 consecutive positive squares in 1 way.
1356 = 340² - 338² = 116² - 110² is the difference of 2 nonnegative squares in 2 ways.
1356 is the difference of 2 positive pentagonal numbers in 1 way.
1356 = 14² + 22² + 26² is the sum of 3 positive squares.
1356² = 180² + 1344² is the sum of 2 positive squares in 1 way.
1356² is the sum of 3 positive squares.
1356 is a proper divisor of 227² - 1.
1356 is palindromic in (at least) the following bases: 15, and -15.
1356 in base 14 = 6cc and consists of only the digits '6' and 'c'.
1356 in base 15 = 606 and consists of only the digits '0' and '6'.
1356 in base 36 = 11o and consists of only the digits '1' and 'o'.

The number 1356 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001934: Expansion of 1/theta_4(q)^2 in powers of q.
A007534: Even numbers that are not the sum of a pair of twin primes.
A018039: Powers of cube root of 22 rounded down.
A018040: Powers of cube root of 22 rounded to nearest integer.
A046741: Triangle read by rows giving number of arrangements of k dumbbells on 2 X n grid (n >= 0, k >= 0).
A111871: Prime gaps q-p with n-th record merit referred to in A111870.
A162532: Numbers n such that their largest divisor <= sqrt(n) equals 12.
A215861: Number T(n,k) of simple labeled graphs on n nodes with exactly k connected components that are trees or cycles; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A250474: Number of times prime(n) occurs as the least prime factor among numbers 1 .. prime(n)^3: a(n) = A078898(A030078(n)).
A298118: Number of unlabeled rooted trees with n nodes in which all positive outdegrees are odd.

Number of the day: 99678

Properties of the number 99678:

99678 = 2 × 3 × 37 × 449 is the 90115^th composite number and is squarefree.
99678 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 32256 totatives.
99678 has an emirpimes digit sum 39 in base 10.
99678 is the difference of 2 positive pentagonal numbers in 3 ways.
99678 = 22² + 35² + 313² is the sum of 3 positive squares.
99678² = 62160² + 77922² = 53550² + 84072² = 33528² + 93870² = 32328² + 94290² is the sum of 2 positive squares in 4 ways.
99678² is the sum of 3 positive squares.
99678 is a proper divisor of 541²⁴ - 1.
99678 is palindromic in (at least) base -11.

The number 99678 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A064262: Values of m such that N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,51.
A248534: Number of length n+3 0..5 arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth.

Number of the day: 544978

Properties of the number 544978:

544978 = 2 × 7² × 67 × 83 is the 500029^th composite number and is not squarefree.
544978 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 227304 totatives.
544978 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 544978 results in a sphenic number.
544978 is the difference of 2 positive pentagonal numbers in 9 ways.
544978 = 9² + 116² + 729² is the sum of 3 positive squares.
544978² is the sum of 3 positive squares.
544978 is a proper divisor of 499⁴² - 1.

Number of the day: 785039

Properties of the number 785039:

785039 is a cyclic number.
785039 = 67 × 11717 is semiprime and squarefree.
785039 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 773256 totatives.
Reversing the decimal digits of 785039 results in a sphenic number.
785039 = 392520² - 392519² = 5892² - 5825² is the difference of 2 nonnegative squares in 2 ways.
785039 is the difference of 2 positive pentagonal numbers in 2 ways.
785039 is not the sum of 3 positive squares.
785039² = 51255² + 783364² is the sum of 2 positive squares in 1 way.
785039² is the sum of 3 positive squares.
785039 is a proper divisor of 401²⁰² - 1.
785039 = '78503' + '9' is the concatenation of 2 semiprime numbers.
785039 is an emirpimes in (at least) the following bases: 5, 6, 11, 13, 14, 15, 16, 17, 22, 23, 31, 32, 34, 39, 43, 44, 46, 47, 49, 55, 59, 61, 63, 64, 67, 69, 70, 72, 74, 75, 76, 77, 81, 92, 94, 95, 96, 98, and 100.

Number of the day: 354515

Properties of the number 354515:

354515 = 5 × 7² × 1447 is the 324176^th composite number and is not squarefree.
354515 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 242928 totatives.
354515 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 354515 results in a sphenic number.
354515 = 177258² - 177257² = 35454² - 35449² = 25326² - 25319² = 5082² - 5047² = 3642² - 3593² = 846² - 601² is the difference of 2 nonnegative squares in 6 ways.
354515 is the difference of 2 positive pentagonal numbers in 6 ways.
354515 = 29² + 45² + 593² is the sum of 3 positive squares.
354515² = 212709² + 283612² is the sum of 2 positive squares in 1 way.
354515² is the sum of 3 positive squares.
354515 is a proper divisor of 743⁸⁴ - 1.
354515 = '3545' + '15' is the concatenation of 2 semiprime numbers.
354515 is palindromic in (at least) base -94.

The number 354515 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A224670: Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent
A278544: Arithmetic derivative of the prime-factorization representation of the n-th Stern polynomial: a(n) = A003415(A260443(n)).

Number of the day: 5799

Properties of the number 5799:

5799 = 3 × 1933 is semiprime and squarefree.
5799 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 3864 totatives.
5799 has a sphenic digit sum 30 in base 10.
5799 has an oblong digit sum 30 in base 10.
5799 = 2900² - 2899² = 968² - 965² is the difference of 2 nonnegative squares in 2 ways.
5799 is the sum of 2 positive triangular numbers.
5799 is the difference of 2 positive pentagonal numbers in 1 way.
5799 is not the sum of 3 positive squares.
5799² = 3276² + 4785² is the sum of 2 positive squares in 1 way.
5799² is the sum of 3 positive squares.
5799 is a proper divisor of 277¹² - 1.
5799 = '579' + '9' is the concatenation of 2 semiprime numbers.
5799 is an emirpimes in (at least) the following bases: 2, 4, 11, 12, 15, 17, 23, 24, 29, 31, 33, 35, 37, 40, 41, 43, 47, 49, 51, 54, 55, 58, 60, 61, 68, 73, 77, 81, 84, 88, 90, 92, 93, 97, and 100.
5799 is palindromic in (at least) the following bases: 42, and -46.
5799 in base 5 = 141144 and consists of only the digits '1' and '4'.
5799 in base 12 = 3433 and consists of only the digits '3' and '4'.
5799 in base 21 = d33 and consists of only the digits '3' and 'd'.
5799 in base 41 = 3II and consists of only the digits '3' and 'I'.
5799 in base 42 = 3C3 and consists of only the digits '3' and 'C'.

The number 5799 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000444: Partially labeled rooted trees with n nodes (3 of which are labeled).
A005821: a(n) = [ tau*a(n-1) ] + a(n-2).
A033681: a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A094362: McKay-Thompson series of class 39C for the Monster group with a(0) = 1.
A098702: Number of self-polar configurations of type (n_3).
A107717: Triangular matrix T, read by rows, that satisfies: SHIFT_LEFT(column 0 of T^((3*p-1)/3) = (3*p-1)*(column p of T), or [T^((3*p-1)/3)](m,0) = (3*p-1)*T(p+m,p) for all m>=1 and p>=0.
A111473: a(1) = 3, a(n) = least k such that concatenation of n copies of k with all previous concatenation gives a prime.
A219519: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 nXk array
A246569: Semiprimes with strictly increasing product of digits.
A268393: Positions of records in permutation A267107.

Number of the day: 54920

Properties of the number 54920:

54920 = 2³ × 5 × 1373 is the 49335^th composite number and is not squarefree.
54920 has 3 distinct prime factors, 16 divisors, 17 antidivisors and 21952 totatives.
54920 has an oblong digit sum 20 in base 10.
54920 = 13731² - 13729² = 6867² - 6863² = 2751² - 2741² = 1383² - 1363² is the difference of 2 nonnegative squares in 4 ways.
54920 is the difference of 2 positive pentagonal numbers in 2 ways.
54920 = 86² + 218² = 62² + 226² is the sum of 2 positive squares in 2 ways.
54920 = 8² + 10² + 234² is the sum of 3 positive squares.
54920² = 37496² + 40128² = 32952² + 43936² = 28024² + 47232² = 5920² + 54600² is the sum of 2 positive squares in 4 ways.
54920² is the sum of 3 positive squares.
54920 is a proper divisor of 1801⁷ - 1.
54920 is palindromic in (at least) the following bases: 47, -88, and -89.
54920 in base 47 = OeO and consists of only the digits 'O' and 'e'.
54920 in base 60 = FFK and consists of only the digits 'F' and 'K'.

The number 54920 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005956: Number of acyclic tertiary alcohols with n carbon atoms.
A067988: Row sums of triangle A067330; also of triangle A067418.
A082095: A 2nd order recursion: a(1)=a(2)=1; a(n)=p[a(n-2)]+Pi[a(n-1)]=A000040[a(n-2)]+A000720[a(n-1)].
A265678: Number of nX3 arrays containing 3 copies of 0..n-1 with no equal vertical or antidiagonal neighbors and new values introduced sequentially from 0.
A265679: T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no equal vertical or antidiagonal neighbors and new values introduced sequentially from 0.
A265682: Number of 5Xn arrays containing n copies of 0..5-1 with no equal vertical or antidiagonal neighbors and new values introduced sequentially from 0.

Number of the day: 467916

Properties of the number 467916:

467916 = 2² × 3 × 38993 is the 428854^th composite number and is not squarefree.
467916 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 155968 totatives.
467916 has a semiprime digit sum 33 in base 10.
467916 = 224² + … + 232² is the sum of at least 2 consecutive positive squares in 1 way.
467916 = 116980² - 116978² = 38996² - 38990² is the difference of 2 nonnegative squares in 2 ways.
467916 is the sum of 2 positive triangular numbers.
467916 is the difference of 2 positive pentagonal numbers in 1 way.
467916 = 26² + 46² + 682² is the sum of 3 positive squares.
467916² = 242100² + 400416² is the sum of 2 positive squares in 1 way.
467916² is the sum of 3 positive squares.
467916 is a proper divisor of 349²⁴³⁷ - 1.

Number of the day: 97994814805986

Properties of the number 97994814805986:

97994814805986 = 2 × 3 × 7² × 19² × 29 × 367 × 86753 is composite and not squarefree.
97994814805986 has 7 distinct prime factors, 288 divisors, 155 antidivisors and 25540183001088 totatives.
97994814805986 has a semiprime digit sum 87 in base 10.
Reversing the decimal digits of 97994814805986 results in a sphenic number.
97994814805986 is the difference of 2 positive pentagonal numbers in 32 ways.
97994814805986 = 404² + 809² + 9899233² is the sum of 3 positive squares.
97994814805986² = 69147494476830² + 69437797606464² = 2594615868936² + 97960459866990² = 2184187306350² + 97970470319736² = 67582630900680² + 70961762445714² is the sum of 2 positive squares in 4 ways.
97994814805986² is the sum of 3 positive squares.
97994814805986 is a proper divisor of 1873^13891164 - 1.

Number of the day: 9821

Properties of the number 9821:

9821 is a cyclic number.
9821 = 7 × 23 × 61 is a sphenic number and squarefree.
9821 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 7920 totatives.
9821 has an oblong digit sum 20 in base 10.
9821 has a Fibonacci digit product 144 in base 10.
Reversing the decimal digits of 9821 results in a prime.
9821 = 4911² - 4910² = 705² - 698² = 225² - 202² = 111² - 50² is the difference of 2 nonnegative squares in 4 ways.
9821 is the sum of 2 positive triangular numbers.
9821 is the difference of 2 positive pentagonal numbers in 3 ways.
9821 = 11² + 40² + 90² is the sum of 3 positive squares.
9821² = 1771² + 9660² is the sum of 2 positive squares in 1 way.
9821² is the sum of 3 positive squares.
9821 is a proper divisor of 47⁶ - 1.
9821 is palindromic in (at least) base -30.
9821 in base 29 = bjj and consists of only the digits 'b' and 'j'.
9821 in base 49 = 44L and consists of only the digits '4' and 'L'.

The number 9821 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A028910: Arrange digits of 2^n in descending order.
A042085: Denominators of continued fraction convergents to sqrt(566).
A050817: Odd numbers seen in decimal expansion of pi (disregarding the decimal period) contiguous, smallest and distinct.
A066509: a(n) is the first of a triple of consecutive integers, each the product of three distinct primes.
A077325: Average of terms of n-th row of A077321.
A081677: Numbers n such that 2*10^n + 3 is prime.
A204663: Numbers n such that n!8 + 2 is prime.
A232206: Triangle read by rows: T(n,k) is the number of non-equivalent regular polygons with n+1 edges, one of which is rooted, which are dissected by non-intersecting diagonals into k regions, such that two such polygons are identified up to reflection along the rooted edge and twisting along the diagonals that does not affect the root edge (for 1 <= k <= n-1 and n>=2).
A244242: Number of partitions of n into 6 parts such that every i-th smallest part (counted with multiplicity) is different from i.
A286006: Numbers n such that 11^n is the highest power of 11 dividing A240751(n).

Number of the day: 353035

George Boole was born on this day 203 years ago.

Properties of the number 353035:

353035 is a cyclic number.
353035 = 5 × 70607 is semiprime and squarefree.
353035 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 282424 totatives.
353035 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 353035 results in a prime.
353035 = 176518² - 176517² = 35306² - 35301² is the difference of 2 nonnegative squares in 2 ways.
353035 is the sum of 2 positive triangular numbers.
353035 is the difference of 2 positive pentagonal numbers in 2 ways.
353035 = 27² + 55² + 591² is the sum of 3 positive squares.
353035² = 211821² + 282428² is the sum of 2 positive squares in 1 way.
353035² is the sum of 3 positive squares.
353035 is a proper divisor of 1721¹⁶⁴² - 1.
353035 = '35' + '3035' is the concatenation of 2 semiprime numbers.
353035 is an emirpimes in (at least) the following bases: 2, 5, 6, 11, 21, 22, 23, 25, 37, 38, 47, 49, 55, 58, 65, 67, 70, 73, 75, 76, 78, 83, 88, 92, and 94.
353035 is palindromic in (at least) base 100.