Number of the day: 875487

Properties of the number 875487:

875487 = 3 × 291829 is semiprime and squarefree.
875487 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 583656 totatives.
875487 has an emirpimes digit sum 39 in base 10.
875487 = 437744² - 437743² = 145916² - 145913² is the difference of 2 nonnegative squares in 2 ways.
875487 is the difference of 2 positive pentagonal numbers in 1 way.
875487 is not the sum of 3 positive squares.
875487² = 233913² + 843660² is the sum of 2 positive squares in 1 way.
875487² is the sum of 3 positive squares.
875487 is a proper divisor of 1777⁴⁹⁸ - 1.
875487 is an emirpimes in (at least) the following bases: 4, 12, 13, 16, 28, 29, 30, 37, 43, 50, 54, 63, 67, 69, 76, 78, 84, 87, 88, 91, 93, 96, and 99.
875487 is palindromic in (at least) base 100.

Number of the day: 753389273

Properties of the number 753389273:

753389273 = 7 × 13 × 19 × 47 × 73 × 127 is the 714520359^th composite number and is squarefree.
753389273 has 6 distinct prime factors, 64 divisors, 69 antidivisors and 540836352 totatives.
753389273 has a prime digit sum 47 in base 10.
Reversing the decimal digits of 753389273 results in a semiprime.
753389273 = 1033³ - 704³ is the difference of 2 positive cubes in 1 way.
753389273 is the difference of 2 nonnegative squares in 32 ways.
753389273 is the sum of 2 positive triangular numbers.
753389273 is the difference of 2 positive pentagonal numbers in 28 ways.
753389273 = 9² + 326² + 27446² is the sum of 3 positive squares.
753389273² = 495379248² + 567622055² = 238956977² + 714489300² = 333428340² + 675589327² = 289765105² + 695436252² is the sum of 2 positive squares in 4 ways.
753389273² is the sum of 3 positive squares.
753389273 is a proper divisor of 659¹⁸ - 1.
753389273 = '75338927' + '3' is the concatenation of 2 prime numbers.
753389273 = '75338' + '9273' is the concatenation of 2 sphenic numbers.

Number of the day: 922125976

Properties of the number 922125976:

922125976 = 2³ × 2311 × 49877 is the 875043347^th composite number and is not squarefree.
922125976 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 460854240 totatives.
922125976 has a prime digit sum 43 in base 10.
Reversing the decimal digits of 922125976 results in a semiprime.
922125976 = 140³ + 326³ + 960³ is the sum of 3 positive cubes in 1 way.
922125976 = 230531495² - 230531493² = 115265749² - 115265745² = 102065² - 97443² = 54499² - 45255² is the difference of 2 nonnegative squares in 4 ways.
922125976 is the difference of 2 positive pentagonal numbers in 3 ways.
922125976 = 726² + 1300² + 30330² is the sum of 3 positive squares.
922125976² = 133945560² + 912345824² is the sum of 2 positive squares in 1 way.
922125976² is the sum of 3 positive squares.
922125976 is a proper divisor of 557²³⁵⁹⁰ - 1.
922125976 = '92212597' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 9979

Properties of the number 9979:

9979 is a cyclic number.
9979 = 17 × 587 is semiprime and squarefree.
9979 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 9376 totatives.
9979 has a semiprime digit sum 34 in base 10.
9979 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 9979 results in an emirpimes.
9979 = 4990² - 4989² = 302² - 285² is the difference of 2 nonnegative squares in 2 ways.
9979 is the difference of 2 positive pentagonal numbers in 2 ways.
9979 = 3² + 13² + 99² is the sum of 3 positive squares.
9979² = 4696² + 8805² is the sum of 2 positive squares in 1 way.
9979² is the sum of 3 positive squares.
9979 is a proper divisor of 137²⁹³ - 1.
9979 = '9' + '979' is the concatenation of 2 semiprime numbers.
9979 is an emirpimes in (at least) the following bases: 9, 10, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 37, 40, 41, 42, 43, 44, 49, 50, 52, 54, 57, 63, 64, 65, 67, 68, 70, 72, 73, 75, 78, 82, 87, 88, 89, 91, 96, 97, 98, 99, and 100.
9979 is palindromic in (at least) the following bases: 36, -6, -57, and -58.
9979 in base 6 = 114111 and consists of only the digits '1' and '4'.
9979 consists of only the digits '7' and '9'.
9979 in base 22 = kdd and consists of only the digits 'd' and 'k'.
9979 in base 36 = 7p7 and consists of only the digits '7' and 'p'.
9979 in base 57 = 344 and consists of only the digits '3' and '4'.

The number 9979 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A041020: Numerators of continued fraction convergents to sqrt(14).
A041228: Numerators of continued fraction convergents to sqrt(126).
A042318: Numerators of continued fraction convergents to sqrt(686).
A042709: Denominators of continued fraction convergents to sqrt(884).
A109936: Composite numbers between largest n-digit prime and the smallest (n+1) digit prime.
A178369: Numbers with rounded up arithmetic mean of digits = 9.
A236082: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
A266775: Molien series for invariants of finite Coxeter group D_12 (bisected).
A274410: Numbers n such that the Collatz iterations for n and n + 1 have the same length (A078417) but do not meet a certain condition. (See comments.)
A292739: Numbers in which 9 outnumbers all other digits together.

Number of the day: 562269

Properties of the number 562269:

562269 = 3 × 187423 is semiprime and squarefree.
562269 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 374844 totatives.
562269 has a sphenic digit sum 30 in base 10.
562269 has an oblong digit sum 30 in base 10.
562269 has an oblong digit product 6480 in base 10.
Reversing the decimal digits of 562269 results in a sphenic number.
562269 = 281135² - 281134² = 93713² - 93710² is the difference of 2 nonnegative squares in 2 ways.
562269 is the sum of 2 positive triangular numbers.
562269 is the difference of 2 positive pentagonal numbers in 1 way.
562269 = 38² + 115² + 740² is the sum of 3 positive squares.
562269² is the sum of 3 positive squares.
562269 is a proper divisor of 7³¹²³⁷ - 1.
562269 is an emirpimes in (at least) the following bases: 3, 15, 20, 27, 46, 49, 55, 66, 69, 72, 78, 83, 85, 87, 90, 91, 93, and 96.
562269 is palindromic in (at least) base -87.

Number of the day: 783569

Properties of the number 783569:

783569 is a cyclic number.
783569 and 783571 form a twin prime pair.
783569 has 29 antidivisors and 783568 totatives.
783569 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 783569 results in a semiprime.
783569 = 391785² - 391784² is the difference of 2 nonnegative squares in 1 way.
783569 is the sum of 2 positive triangular numbers.
783569 is the difference of 2 positive pentagonal numbers in 1 way.
783569 = 188² + 865² is the sum of 2 positive squares in 1 way.
783569 = 32² + 33² + 884² is the sum of 3 positive squares.
783569² = 325240² + 712881² is the sum of 2 positive squares in 1 way.
783569² is the sum of 3 positive squares.
783569 is a proper divisor of 199⁴⁸⁹⁷³ - 1.
783569 = '7835' + '69' is the concatenation of 2 semiprime numbers.
783569 is an emirp in (at least) the following bases: 2, 5, 7, 19, 21, 34, 45, 53, 59, 61, 67, 73, 76, 79, 81, 85, 86, 89, 90, 95, and 98.

Number of the day: 4449

Joseph-Louis Lagrange was born on this day 282 years ago.

Properties of the number 4449:

4449 = 3 × 1483 is semiprime and squarefree.
4449 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2964 totatives.
4449 has a semiprime digit sum 21 in base 10.
4449 has a Fibonacci digit sum 21 in base 10.
4449 has a triangular digit sum 21 in base 10.
4449 = 2225² - 2224² = 743² - 740² is the difference of 2 nonnegative squares in 2 ways.
4449 is the sum of 2 positive triangular numbers.
4449 is the difference of 2 positive pentagonal numbers in 1 way.
4449 = 8² + 17² + 64² is the sum of 3 positive squares.
4449² is the sum of 3 positive squares.
4449 is a proper divisor of 577¹³ - 1.
4449 is an emirpimes in (at least) the following bases: 3, 5, 6, 9, 13, 14, 18, 20, 21, 22, 24, 28, 31, 37, 39, 48, 49, 50, 52, 54, 59, 60, 63, 73, 77, 78, 79, 85, 86, 91, 96, 97, and 98.
4449 is palindromic in (at least) the following bases: 38, -4, -35, and -39.
4449 in base 6 = 32333 and consists of only the digits '2' and '3'.
4449 consists of only the digits '4' and '9'.
4449 in base 16 = 1161 and consists of only the digits '1' and '6'.
4449 in base 18 = dd3 and consists of only the digits '3' and 'd'.
4449 in base 37 = 399 and consists of only the digits '3' and '9'.
4449 in base 38 = 333 and consists of only the digit '3'.

The number 4449 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003294: Numbers n such that n^4 can be written as a sum of four positive 4th powers.
A010919: Pisot sequence T(4,13), a(n) = floor(a(n-1)^2/a(n-2)).
A053445: Second differences of partition numbers A000041.
A096739: Numbers n such that n^4 can be written as a sum of four distinct positive 4th powers.
A107342: Semiprimes with semiprime digits (digits 4, 6, 9 only).
A107665: Numbers with semiprime digits (digits 4, 6, 9 only).
A112472: Number of partitions of n which represent first player winning Chomp positions with unique winning moves.
A160644: First of two sequences bisecting the second differences of the partition numbers (see A053445).
A188948: Values of x such that x^2 + y^2 = 13^n with x and y coprime and 0 < x < y.
A292734: Numbers in which 4 outnumbers all other digits together.

Number of the day: 3101061305

Properties of the number 3101061305:

3101061305 = 5 × 620212261 is semiprime and squarefree.
3101061305 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2480849040 totatives.
3101061305 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 3101061305 results in a prime.
3101061305 = 1550530653² - 1550530652² = 310106133² - 310106128² is the difference of 2 nonnegative squares in 2 ways.
3101061305 is the difference of 2 positive pentagonal numbers in 2 ways.
3101061305 = 35156² + 43187² = 13456² + 54037² is the sum of 2 positive squares in 2 ways.
3101061305 = 39² + 1010² + 55678² is the sum of 3 positive squares.
3101061305² = 1860636783² + 2480849044² = 1454243744² + 2738933433² = 629172633² + 3036564344² = 1318600500² + 2806755055² is the sum of 2 positive squares in 4 ways.
3101061305² is the sum of 3 positive squares.
3101061305 is a proper divisor of 431^10336871 - 1.
3101061305 = '3101061' + '305' is the concatenation of 2 semiprime numbers.
3101061305 = '310' + '1061305' is the concatenation of 2 sphenic numbers.
3101061305 is an emirpimes in (at least) the following bases: 2, 8, 12, 13, 15, 22, 33, 35, 43, 51, 55, 69, 70, 74, 76, 78, 83, 88, 90, 93, 95, and 98.

Number of the day: 66928017519

David Hilbert was born on this day 156 years ago.

Properties of the number 66928017519:

66928017519 = 3² × 11 × 17 × 397 × 100169 is composite and not squarefree.
66928017519 has 5 distinct prime factors, 48 divisors, 55 antidivisors and 38079866880 totatives.
66928017519 is the difference of 2 nonnegative squares in 24 ways.
66928017519 is the difference of 2 positive pentagonal numbers in 7 ways.
66928017519 is not the sum of 3 positive squares.
66928017519² = 31495537656² + 59054133105² = 25268095215² + 61974856944² = 37390319505² + 55509670656² = 30255946281² + 59698720620² = 23968891980² + 62488812969² = 36223432740² + 56278081431² = 8131719420² + 66432180969² = 1270405719² + 66915959220² = 14907144681² + 65246736060² = 38437249356² + 54789938775² = 32610809385² + 58445655444² = 43857709335² + 50555522556² = 6869260431² + 66574565640² is the sum of 2 positive squares in 13 ways.
66928017519² is the sum of 3 positive squares.
66928017519 is a proper divisor of 971⁷⁹⁰⁸⁰ - 1.
66928017519 = '6692801' + '7519' is the concatenation of 2 semiprime numbers.

Number of the day: 157757

Properties of the number 157757:

157757 = 19³ × 23 is the 143255^th composite number and is not squarefree.
157757 has 2 distinct prime factors, 8 divisors, 19 antidivisors and 142956 totatives.
Reversing the decimal digits of 157757 results in a prime.
157757 = 78879² - 78878² = 4161² - 4142² = 3441² - 3418² = 399² - 38² is the difference of 2 nonnegative squares in 4 ways.
157757 is the difference of 2 positive pentagonal numbers in 3 ways.
157757 = 10² + 29² + 396² is the sum of 3 positive squares.
157757² is the sum of 3 positive squares.
157757 is a proper divisor of 1151⁵⁷ - 1.
157757 = '157' + '757' is the concatenation of 2 prime numbers.
157757 = '1577' + '57' is the concatenation of 2 semiprime numbers.

Number of the day: 7775

Properties of the number 7775:

7775 = 5² × 311 is the 6789^th composite number and is not squarefree.
7775 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 6200 totatives.
7775 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7775 results in a semiprime.
7775 = 6⁵ - 1⁵ is the difference of 2 positive fifth powers in 1 way.
7775 = 3888² - 3887² = 780² - 775² = 168² - 143² is the difference of 2 nonnegative squares in 3 ways.
7775 is the difference of 2 positive pentagonal numbers in 3 ways.
7775 is not the sum of 3 positive squares.
7775² = 4665² + 6220² = 2177² + 7464² is the sum of 2 positive squares in 2 ways.
7775² is the sum of 3 positive squares.
7775 is a proper divisor of 881¹⁰ - 1.
7775 is palindromic in (at least) the following bases: 6, 37, -42, and -58.
7775 in base 6 = 55555 and consists of only the digit '5'.
7775 consists of only the digits '5' and '7'.
7775 in base 36 = 5zz and consists of only the digits '5' and 'z'.
7775 in base 37 = 5P5 and consists of only the digits '5' and 'P'.

The number 7775 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014946: Numbers n such that n divides 6^n-1.
A024062: a(n) = 6^n-1.
A037205: a(n) = (n+1)^n - 1.
A079907: Numbers n such that 11*12^n -1 is prime.
A104621: Heptanacci-Lucas numbers.
A116632: Positive integers n such that 13^n == 7 (mod n).
A140811: 6n^2 - 1.
A141530: 4*n^3-6*n^2+1
A181288: Numbers of the form i*6^j-1 (i=1..5, j >= 0).
A292737: Numbers in which 7 outnumbers all other digits together.

Number of the day: 21928

Properties of the number 21928:

21928 = 2³ × 2741 is the 19470^th composite number and is not squarefree.
21928 has 2 distinct prime factors, 8 divisors, 21 antidivisors and 10960 totatives.
21928 has a semiprime digit sum 22 in base 10.
21928 = 5483² - 5481² = 2743² - 2739² is the difference of 2 nonnegative squares in 2 ways.
21928 is the difference of 2 positive pentagonal numbers in 2 ways.
21928 = 42² + 142² is the sum of 2 positive squares in 1 way.
21928 = 78² + 88² + 90² is the sum of 3 positive squares.
21928² = 11928² + 18400² is the sum of 2 positive squares in 1 way.
21928² is the sum of 3 positive squares.
21928 is a proper divisor of 449²⁰ - 1.
21928 is palindromic in (at least) the following bases: -35, and -84.
21928 in base 28 = rr4 and consists of only the digits '4' and 'r'.
21928 in base 34 = iww and consists of only the digits 'i' and 'w'.

The number 21928 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002257: Numbers n such that 13*4^n + 1 is prime.
A036063: Increasing gaps among twin primes: size.
A075454: Integer averages of two successive perfect powers (pp(n) + pp(n+1))/2.
A093928: a(n) = sum( A073698(k), k=1...n )^(1/n).
A198016: Number of isomorphism classes of nanocones with 4 pentagons and a nearsymmetric boundary of length n
A233075: Numbers that are midway between the nearest square and the nearest cube.
A235893: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
A238869: Number of partitions of n where the difference between consecutive parts is at most 9.
A252201: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 3 5 6 or 7
A261228: a(n) = number of steps to reach 0 when starting from k = (n^3)-1 and repeatedly applying the map that replaces k with k - A055401(k), where A055401(k) = the number of positive cubes needed to sum to k using the greedy algorithm.

Number of the day: 56620484836

Properties of the number 56620484836:

56620484836 = 2² × 5507 × 2570387 is composite and not squarefree.
56620484836 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 28305090632 totatives.
Reversing the decimal digits of 56620484836 results in a sphenic number.
56620484836 = 14155121210² - 14155121208² = 2575894² - 2564880² is the difference of 2 nonnegative squares in 2 ways.
56620484836 is the sum of 2 positive triangular numbers.
56620484836 is the difference of 2 positive pentagonal numbers in 2 ways.
56620484836 = 2534² + 3456² + 237912² is the sum of 3 positive squares.
56620484836² is the sum of 3 positive squares.
56620484836 is a proper divisor of 641^14530334 - 1.

Number of the day: 103841936

Properties of the number 103841936:

103841936 = 2⁴ × 11 × 167 × 3533 is the 97872092^th composite number and is not squarefree.
103841936 has 4 distinct prime factors, 40 divisors, 13 antidivisors and 46904960 totatives.
103841936 has a semiprime digit sum 35 in base 10.
103841936 = 30³ + 294³ + 428³ = 65³ + 239³ + 448³ is the sum of 3 positive cubes in 2 ways.
103841936 is the difference of 2 nonnegative squares in 12 ways.
103841936 is the difference of 2 positive pentagonal numbers in 4 ways.
103841936 = 316² + 824² + 10152² is the sum of 3 positive squares.
103841936² = 44323136² + 93907440² is the sum of 2 positive squares in 1 way.
103841936² is the sum of 3 positive squares.
103841936 is a proper divisor of 1669¹⁷⁶⁶⁰ - 1.
103841936 = '10384193' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 475395

Properties of the number 475395:

475395 = 3 × 5 × 41 × 773 is the 435744^th composite number and is squarefree.
475395 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 247040 totatives.
475395 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 475395 results in a sphenic number.
475395 = 237698² - 237697² = 79234² - 79231² = 47542² - 47537² = 15854² - 15839² = 5818² - 5777² = 1994² - 1871² = 1262² - 1057² = 694² - 79² is the difference of 2 nonnegative squares in 8 ways.
475395 is the difference of 2 positive pentagonal numbers in 3 ways.
475395 = 7² + 25² + 689² is the sum of 3 positive squares.
475395² = 194796² + 433653² = 79101² + 468768² = 297891² + 370488² = 104355² + 463800² = 16020² + 475125² = 217980² + 422475² = 308427² + 361764² = 207192² + 427869² = 272259² + 389712² = 285237² + 380316² = 180072² + 439971² = 296061² + 371952² = 119925² + 460020² is the sum of 2 positive squares in 13 ways.
475395² is the sum of 3 positive squares.
475395 is a proper divisor of 1229⁴ - 1.

Number of the day: 66544594533846

Properties of the number 66544594533846:

66544594533846 = 2 × 3² × 11² × 13 × 23² × 89 × 49919 is composite and not squarefree.
66544594533846 has 7 distinct prime factors, 432 divisors, 217 antidivisors and 17604169735680 totatives.
66544594533846 has an oblong digit sum 72 in base 10.
66544594533846 is the difference of 2 positive pentagonal numbers in 33 ways.
66544594533846 = 11870² + 23339² + 8157445² is the sum of 3 positive squares.
66544594533846² = 25594074820710² + 61425779569704² = 3911004691704² + 66429564984090² = 43998802781670² + 49922824594104² = 29159990863146² + 59815365873120² is the sum of 2 positive squares in 4 ways.
66544594533846² is the sum of 3 positive squares.
66544594533846 is a proper divisor of 263¹⁴⁹⁷⁵⁴ - 1.
66544594533846 = '66544594' + '533846' is the concatenation of 2 sphenic numbers.

Number of the day: 5493

Sofia Kovalevskaya was born on this day 168 years ago.

Properties of the number 5493:

5493 = 3 × 1831 is semiprime and squarefree.
5493 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 3660 totatives.
5493 has a semiprime digit sum 21 in base 10.
5493 has a Fibonacci digit sum 21 in base 10.
5493 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 5493 results in a sphenic number.
5493 = 2747² - 2746² = 917² - 914² is the difference of 2 nonnegative squares in 2 ways.
5493 is the difference of 2 positive pentagonal numbers in 1 way.
5493 = 1² + 4² + 74² is the sum of 3 positive squares.
5493² is the sum of 3 positive squares.
5493 is a proper divisor of 571⁵ - 1.
5493 is an emirpimes in (at least) the following bases: 5, 6, 7, 8, 15, 16, 18, 19, 25, 29, 33, 37, 49, 53, 55, 56, 57, 62, 63, 69, 72, 77, 79, 85, 91, and 96.
5493 is palindromic in (at least) the following bases: 20, 21, -31, and -45.
5493 in base 4 = 1111311 and consists of only the digits '1' and '3'.
5493 in base 11 = 4144 and consists of only the digits '1' and '4'.
5493 in base 20 = ded and consists of only the digits 'd' and 'e'.
5493 in base 21 = c9c and consists of only the digits '9' and 'c'.
5493 in base 30 = 633 and consists of only the digits '3' and '6'.

The number 5493 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005421: Number of numbers of complexity n.
A202889: T(n,k)=Number of nXk 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor
A216211: Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with n rows and 4 columns.
A220153: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array
A267019: T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any northeast or northwest neighbors modulo n and the upper left element equal to 0.
A271465: Array read by antidiagonals: T(n,m) = number of self-avoiding walks of any length from NW to SW corners on a grid with n rows and m columns.
A278978: Number of initial digits of ternary Pi wherein the digit counts of zeros and twos are exactly equal.
A279144: Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 137", based on the 5-celled von Neumann neighborhood.
A280147: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 243", based on the 5-celled von Neumann neighborhood.
A284140: Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 805", based on the 5-celled von Neumann neighborhood.

Number of the day: 7277

Alfred Tarski was born on this day 117 years ago.

Properties of the number 7277:

7277 is a cyclic number.
7277 = 19 × 383 is semiprime and squarefree.
7277 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 6876 totatives.
7277 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 7277 results in a prime.
7277 = 3639² - 3638² = 201² - 182² is the difference of 2 nonnegative squares in 2 ways.
7277 is the difference of 2 positive pentagonal numbers in 2 ways.
7277 = 6² + 29² + 80² is the sum of 3 positive squares.
7277² is the sum of 3 positive squares.
7277 is a proper divisor of 1531⁶ - 1.
7277 = '7' + '277' is the concatenation of 2 prime numbers.
7277 is an emirpimes in (at least) the following bases: 5, 7, 16, 17, 23, 25, 29, 32, 34, 37, 45, 46, 55, 57, 59, 60, 61, 64, 65, 66, 67, 69, 71, 72, 73, 76, 77, 78, 79, 81, 85, 87, 93, and 94.
7277 is palindromic in (at least) the following bases: 36, 68, and -75.
7277 consists of only the digits '2' and '7'.
7277 in base 15 = 2252 and consists of only the digits '2' and '5'.
7277 in base 35 = 5ww and consists of only the digits '5' and 'w'.
7277 in base 36 = 5m5 and consists of only the digits '5' and 'm'.

The number 7277 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A049114: 2-ranks of difference sets constructed from Glynn type II hyperovals.
A050969: Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.
A116698: Expansion of -(1-x+3*x^2+x^3)/((x^2+x-1)*(2*x^2+1)).
A186656: Total number of n-digit numbers requiring 5 positive biquadrates in their representation as sum of biquadrates.
A187265: Number of nonempty subsets of {1, 2, ..., n} with <= 4 pairwise coprime elements.
A266338: G.f. = b(2)*b(4)*b(6)/(x^8-x^3-x+1), where b(k) = (1-x^k)/(1-x).
A284921: Numbers with digits 2 and 7 only.
A285338: Expansion of Product_{k>=1} (1 + x^(5*k-4))^(5*k-4).
A292094: Consider Watanabe's 3-shift tag system {00/1011} applied to the word (100)^n; a(n) = position of the longest word in the orbit, or -1 if the orbit is unbounded.
A292737: Numbers in which 7 outnumbers all other digits together.

Number of the day: 258258

Properties of the number 258258:

258258 = 2 × 3 × 7 × 11 × 13 × 43 is the 235561^th composite number and is squarefree.
258258 has 6 distinct prime factors, 64 divisors, 37 antidivisors and 60480 totatives.
258258 has a sphenic digit sum 30 in base 10.
258258 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 258258 results in an oblong number.
258258 = 1³ + 49³ + 52³ is the sum of 3 positive cubes in 1 way.
258258 is the sum of 2 positive triangular numbers.
258258 is the difference of 2 positive pentagonal numbers in 8 ways.
258258 = 59² + 76² + 499² is the sum of 3 positive squares.
258258² = 99330² + 238392² is the sum of 2 positive squares in 1 way.
258258² is the sum of 3 positive squares.
258258 is a proper divisor of 859⁶ - 1.
258258 = '25' + '8258' is the concatenation of 2 semiprime numbers.
258258 = '258' + '258' is the concatenation of 2 sphenic numbers.

Number of the day: 4508836825

Properties of the number 4508836825:

4508836825 = 5² × 139 × 1297507 is the 4295924941^th composite number and is not squarefree.
4508836825 has 3 distinct prime factors, 12 divisors, 41 antidivisors and 3581116560 totatives.
4508836825 has an emirpimes digit sum 49 in base 10.
4508836825 = 2254418413² - 2254418412² = 450883685² - 450883680² = 90176749² - 90176724² = 16218907² - 16218768² = 3244115² - 3243420² = 650491² - 647016² is the difference of 2 nonnegative squares in 6 ways.
4508836825 is the sum of 2 positive triangular numbers.
4508836825 is the difference of 2 positive pentagonal numbers in 6 ways.
4508836825 = 790² + 1113² + 67134² is the sum of 3 positive squares.
4508836825² = 2705302095² + 3607069460² = 1262474311² + 4328483352² is the sum of 2 positive squares in 2 ways.
4508836825² is the sum of 3 positive squares.
4508836825 is a proper divisor of 599^1297506 - 1.

Number of the day: 13120

Properties of the number 13120:

13120 = 2⁶ × 5 × 41 is the 11559^th composite number and is not squarefree.
13120 has 3 distinct prime factors, 28 divisors, 7 antidivisors and 5120 totatives.
13120 has a prime digit sum 7 in base 10.
13120 is the difference of 2 nonnegative squares in 10 ways.
13120 is the difference of 2 positive pentagonal numbers in 1 way.
13120 = 48² + 104² = 24² + 112² is the sum of 2 positive squares in 2 ways.
13120 = 40² + 48² + 96² is the sum of 3 positive squares.
13120² = 5376² + 11968² = 2880² + 12800² = 8512² + 9984² = 7872² + 10496² is the sum of 2 positive squares in 4 ways.
13120² is the sum of 3 positive squares.
13120 is a proper divisor of 337⁴ - 1.
13120 is palindromic in (at least) the following bases: 3, 25, 28, and -38.
13120 in base 3 = 122222221 and consists of only the digits '1' and '2'.
13120 in base 5 = 404440 and consists of only the digits '0' and '4'.
13120 in base 25 = kok and consists of only the digits 'k' and 'o'.
13120 in base 28 = gkg and consists of only the digits 'g' and 'k'.
13120 in base 34 = bbu and consists of only the digits 'b' and 'u'.
13120 in base 40 = 880 and consists of only the digits '0' and '8'.

The number 13120 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000141: Number of ways of writing n as a sum of 6 squares.
A006503: a(n) = n*(n+1)*(n+8)/6.
A006885: Record highest point of trajectory before reaching 1 in `3x+1' problem, corresponding to starting values in A006884.
A035008: Total number of possible knight moves on an (n+2) X (n+2) chessboard, if the knight is placed anywhere.
A077635: LCM of terms in periodic part of continued fraction expansion of square root of -1+3^n.
A087701: Maximal term in Collatz-iteration started at -1+2^n.
A100774: a(n) = 2*(3^n - 1).
A137491: Numbers with 28 divisors.
A164123: Partial sums of A162436.
A179672: Products of the 6st power of a prime and 2 distinct primes (p^6*q*r).

Number of the day: 65295

Properties of the number 65295:

65295 = 3² × 5 × 1451 is the 58771^th composite number and is not squarefree.
65295 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 34800 totatives.
65295 = 23³ + 24³ + 34³ is the sum of 3 positive cubes in 1 way.
65295 = 32648² - 32647² = 10884² - 10881² = 6532² - 6527² = 3632² - 3623² = 2184² - 2169² = 748² - 703² is the difference of 2 nonnegative squares in 6 ways.
65295 is the difference of 2 positive pentagonal numbers in 2 ways.
65295 is not the sum of 3 positive squares.
65295² = 39177² + 52236² is the sum of 2 positive squares in 1 way.
65295² is the sum of 3 positive squares.
65295 is a proper divisor of 739¹⁰ - 1.
65295 = '6529' + '5' is the concatenation of 2 prime numbers.
65295 = '65' + '295' is the concatenation of 2 semiprime numbers.
65295 is palindromic in (at least) the following bases: 49, 64, 76, 81, and -68.
65295 in base 4 = 33330033 and consists of only the digits '0' and '3'.
65295 in base 16 = ff0f and consists of only the digits '0' and 'f'.
65295 in base 49 = R9R and consists of only the digits '9' and 'R'.

The number 65295 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A097262: Numbers whose set of base 16 digits is {0,F}, where F base 16 = 15 base 10.
A243579: Integers of the form 8k+7 that can be written as a sum of four distinct squares of the form m, m+2, m+4, m+5, where m == 1 (mod 4).
A289533: Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 587", based on the 5-celled von Neumann neighborhood.

Number of the day: 71370

Properties of the number 71370:

71370 = 2 × 3² × 5 × 13 × 61 is the 64301^th composite number and is not squarefree.
71370 has 5 distinct prime factors, 48 divisors, 27 antidivisors and 17280 totatives.
71370 = 68² + … + 80² is the sum of at least 2 consecutive positive squares in 1 way.
71370 is the difference of 2 positive pentagonal numbers in 3 ways.
71370 = 111² + 243² = 9² + 267² = 153² + 219² = 57² + 261² is the sum of 2 positive squares in 4 ways.
71370 = 8² + 65² + 259² is the sum of 3 positive squares.
71370² = 31824² + 63882² = 4806² + 71208² = 46728² + 53946² = 15120² + 69750² = 12870² + 70200² = 38880² + 59850² = 48438² + 52416² = 24552² + 67014² = 29754² + 64872² = 42822² + 57096² = 17568² + 69174² = 36234² + 61488² = 27450² + 65880² is the sum of 2 positive squares in 13 ways.
71370² is the sum of 3 positive squares.
71370 is a proper divisor of 233⁴ - 1.
71370 is palindromic in (at least) the following bases: 8, 52, 67, and -71.
71370 in base 46 = XXO and consists of only the digits 'O' and 'X'.
71370 in base 52 = QKQ and consists of only the digits 'K' and 'Q'.

The number 71370 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A069520: (1/n)*sum(d|n,d*sigma(d)) is an integer.
A127535: Triangle read by rows: T(n,k) is the number of even trees with 2n edges and jump-length equal to k (0<=k<=n-1). An even tree is an ordered tree in which each vertex has an even outdegree. In the preorder traversal of an ordered tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump; the positive difference of the levels is called the jump distance; the sum of the jump distances in a given ordered tree is called the jump-length.
A233246: Sum of squares of cycle lengths for different cycles in Fibonacci-like sequences modulo n.
A248083: Subsequence of lesser of 2 terms of A095301 that are 2 apart.

Number of the day: 763309

Richard Courant was born on this day 130 years ago.

Properties of the number 763309:

763309 is a cyclic number.
763309 = 29 × 26321 is semiprime and squarefree.
763309 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 736960 totatives.
763309 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 763309 results in a prime.
763309 = 40³ + 44³ + 85³ is the sum of 3 positive cubes in 1 way.
763309 = 381655² - 381654² = 13175² - 13146² is the difference of 2 nonnegative squares in 2 ways.
763309 is the difference of 2 positive pentagonal numbers in 2 ways.
763309 = 422² + 765² = 222² + 845² is the sum of 2 positive squares in 2 ways.
763309 = 147² + 190² + 840² is the sum of 3 positive squares.
763309² = 407141² + 645660² = 186760² + 740109² = 375180² + 664741² = 526420² + 552741² is the sum of 2 positive squares in 4 ways.
763309² is the sum of 3 positive squares.
763309 is a proper divisor of 1291²⁸ - 1.
763309 = '763' + '309' is the concatenation of 2 semiprime numbers.
763309 is an emirpimes in (at least) the following bases: 4, 7, 8, 12, 13, 14, 16, 17, 19, 22, 25, 32, 37, 40, 41, 42, 49, 52, 53, 55, 63, 64, 69, 73, 74, 78, 79, 83, 85, 87, 89, 90, 91, 95, 96, and 97.

The number 763309 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A202009: Number of -n..n circular arrays x(0..6) of 7 elements with zero sums of x(i) and x(i)*x((i+1) mod 7)

Number of the day: 534939

Properties of the number 534939:

534939 = 3 × 17² × 617 is the 490743^th composite number and is not squarefree.
534939 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 335104 totatives.
534939 has a semiprime digit sum 33 in base 10.
534939 = 267470² - 267469² = 89158² - 89155² = 15742² - 15725² = 5270² - 5219² = 1070² - 781² = 742² - 125² is the difference of 2 nonnegative squares in 6 ways.
534939 is the sum of 2 positive triangular numbers.
534939 is the difference of 2 positive pentagonal numbers in 2 ways.
534939 = 17² + 95² + 725² is the sum of 3 positive squares.
534939² = 298011² + 444240² = 218064² + 488475² = 369264² + 387045² = 251736² + 472005² = 167739² + 507960² = 328389² + 422280² = 91035² + 527136² is the sum of 2 positive squares in 7 ways.
534939² is the sum of 3 positive squares.
534939 is a proper divisor of 1669¹⁶ - 1.
534939 = '5' + '34939' is the concatenation of 2 prime numbers.
534939 = '5349' + '39' is the concatenation of 2 semiprime numbers.
534939 is palindromic in (at least) base 98.

Number of the day: 45388

Properties of the number 45388:

45388 = 2² × 7 × 1621 is the 40679^th composite number and is not squarefree.
45388 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 19440 totatives.
45388 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 45388 results in a sphenic number.
45388 = 11348² - 11346² = 1628² - 1614² is the difference of 2 nonnegative squares in 2 ways.
45388 is the sum of 2 positive triangular numbers.
45388 is the difference of 2 positive pentagonal numbers in 2 ways.
45388 = 10² + 78² + 198² is the sum of 3 positive squares.
45388² = 21840² + 39788² is the sum of 2 positive squares in 1 way.
45388² is the sum of 3 positive squares.
45388 is a proper divisor of 307¹⁰ - 1.
45388 is palindromic in (at least) the following bases: 40, -44, and -64.
45388 in base 38 = VGG and consists of only the digits 'G' and 'V'.
45388 in base 40 = SES and consists of only the digits 'E' and 'S'.
45388 in base 43 = ONN and consists of only the digits 'N' and 'O'.
45388 in base 61 = CC4 and consists of only the digits '4' and 'C'.

The number 45388 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A111948: Admirable Harshad numbers n such that the subtracted divisor is equal to the digital sum of n.
A118471: a(0)=1. a(n) = a(n-1)*(n+1), if n is in the sequence. a(n)= a(n-1) +1, if n is missing from the sequence.

Number of the day: 1101

Camille Jordan was born on this day 180 years ago.

Properties of the number 1101:

1101 = 3 × 367 is semiprime and squarefree.
1101 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 732 totatives.
1101 has a prime digit sum 3 in base 10.
1101 has a Fibonacci digit sum 3 in base 10.
1101 has a triangular digit sum 3 in base 10.
Reversing the decimal digits of 1101 results in an emirpimes.
1101 = 551² - 550² = 185² - 182² is the difference of 2 nonnegative squares in 2 ways.
1101 is the sum of 2 positive triangular numbers.
1101 is the difference of 2 positive pentagonal numbers in 1 way.
1101 = 11² + 14² + 28² is the sum of 3 positive squares.
1101² is the sum of 3 positive squares.
1101 is a proper divisor of 733² - 1.
1101 is an emirpimes in (at least) the following bases: 3, 7, 9, 10, 11, 12, 17, 21, 29, 31, 33, 35, 41, 44, 48, 49, 52, 54, 59, 61, 62, 64, 65, 66, 67, 69, 71, 72, 73, 75, 81, 83, 87, 89, 91, 93, 95, 96, 97, 99, and 100.
1101 is palindromic in (at least) the following bases: 18, 25, -44, -50, -55, and -100.
1101 consists of only the digits '0' and '1'.
1101 in base 11 = 911 and consists of only the digits '1' and '9'.
1101 in base 12 = 779 and consists of only the digits '7' and '9'.
1101 in base 13 = 669 and consists of only the digits '6' and '9'.
1101 in base 16 = 44d and consists of only the digits '4' and 'd'.
1101 in base 17 = 3dd and consists of only the digits '3' and 'd'.
1101 in base 18 = 373 and consists of only the digits '3' and '7'.
1101 in base 24 = 1ll and consists of only the digits '1' and 'l'.
1101 in base 25 = 1j1 and consists of only the digits '1' and 'j'.

The number 1101 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004676: Primes written in base 2.
A004685: Fibonacci numbers written in base 2.
A007088: The binary numbers: numbers written in base 2.
A007089: Numbers in base 3.
A007623: Integers written in factorial base.
A014418: Representation of n in base of Catalan numbers (a classic greedy version).
A049345: n written in primorial base.
A052217: Numbers whose sum of digits is 3.
A058943: Coefficients of irreducible polynomials over GF(2) listed in lexicographic order.
A061909: Skinny numbers: numbers n such that there are no carries when n is squared by "long multiplication".

Number of the day: 507213

Sir Isaac Newton was born on this day 375 years ago.

Properties of the number 507213:

507213 = 3² × 7 × 83 × 97 is the 465127^th composite number and is not squarefree.
507213 has 4 distinct prime factors, 24 divisors, 29 antidivisors and 283392 totatives.
507213 = 17³ + 21³ + 79³ = 3³ + 37³ + 77³ is the sum of 3 positive cubes in 2 ways.
507213 is the difference of 2 nonnegative squares in 12 ways.
507213 is the difference of 2 positive pentagonal numbers in 2 ways.
507213 = 10² + 13² + 712² is the sum of 3 positive squares.
507213² = 339885² + 376488² is the sum of 2 positive squares in 1 way.
507213² is the sum of 3 positive squares.
507213 is a proper divisor of 1163⁶ - 1.
507213 = '50721' + '3' is the concatenation of 2 triangular numbers.
507213 is palindromic in (at least) base -90.
507213 in base 38 = 999R and consists of only the digits '9' and 'R'.

Number of the day: 2018

Happy New Year!

Properties of the number 2018:

2018 = 2 × 1009 is semiprime and squarefree.
2018 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 1008 totatives.
2018 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 2018 results in an emirpimes.
2018 = 7² + … + 18² is the sum of at least 2 consecutive positive squares in 1 way.
2018 = 13² + 43² is the sum of 2 positive squares in 1 way.
2018 = 9² + 16² + 41² is the sum of 3 positive squares.
2018² = 1118² + 1680² is the sum of 2 positive squares in 1 way.
2018² is the sum of 3 positive squares.
2018 is a proper divisor of 1549⁴ - 1.
2018 is an emirpimes in (at least) the following bases: 5, 8, 10, 11, 12, 13, 14, 17, 19, 21, 22, 25, 27, 29, 31, 38, 42, 45, 46, 49, 55, 57, 63, 65, 67, 69, 74, 76, 78, 80, 83, 85, 87, 90, 91, 95, 96, and 97.
2018 is palindromic in (at least) the following bases: 15, 28, -31, -32, -36, and -42.
2018 in base 3 = 2202202 and consists of only the digits '0' and '2'.
2018 in base 15 = 8e8 and consists of only the digits '8' and 'e'.
2018 in base 27 = 2kk and consists of only the digits '2' and 'k'.
2018 in base 28 = 2g2 and consists of only the digits '2' and 'g'.
2018 in base 31 = 233 and consists of only the digits '2' and '3'.
2018 in base 44 = 11c and consists of only the digits '1' and 'c'.

The number 2018 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000607: Number of partitions of n into prime parts.
A033816: a(n) = 2*n^2 + 3*n + 3.
A050053: a(n) = a(n-1)+a(m), where m=2^(p+1)+2-n and 2^p<n-1<=2^(p+1), for n >= 4.
A077068: Semiprimes of form prime + 1.
A087854: Triangle read by rows: T(n,k) is the number of n-bead necklaces with exactly k different colored beads.
A112844: Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.
A159051: Numbers n such that Fibonacci(n-2) is divisible by n.
A184535: a(n) = floor(3/5 * n^2), with a(1)=1.
A204631: Expansion of 1/(1 - x - x^2 + x^5 - x^7).
A252334: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 3 5 6 or 8 and every 3X3 diagonal and antidiagonal sum not equal to 0 3 5 6 or 8