Number of the day: 8167

Pierre Joseph Louis Fatou was born on this day 140 years ago.

Properties of the number 8167:

8167 is a cyclic number.
8167 is the 1025^th prime.
8167 has 23 antidivisors and 8166 totatives.
8167 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 8167 results in a sphenic number.
8167 = 4084² - 4083² is the difference of 2 nonnegative squares in 1 way.
8167 is the difference of 2 positive pentagonal numbers in 1 way.
8167 is not the sum of 3 positive squares.
8167² is the sum of 3 positive squares.
8167 is a proper divisor of 2¹³⁶¹ - 1.
8167 is an emirp in (at least) the following bases: 16, 23, 25, 27, 29, 33, 35, 41, 47, 49, 57, 66, 67, 73, 74, 76, 78, 79, 81, 85, 88, 91, 96, 99, and 100.
8167 is palindromic in (at least) the following bases: 32, 34, 52, -21, and -71.
8167 in base 32 = 7v7 and consists of only the digits '7' and 'v'.
8167 in base 33 = 7gg and consists of only the digits '7' and 'g'.
8167 in base 34 = 727 and consists of only the digits '2' and '7'.
8167 in base 51 = 377 and consists of only the digits '3' and '7'.
8167 in base 52 = 313 and consists of only the digits '1' and '3'.

The number 8167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002846: Number of ways of transforming a set of n indistinguishable objects into n singletons via a sequence of n-1 refinements.
A039726: Recursive prime generating sequence.
A045714: Primes with first digit 8.
A051439: a(n) = prime(2^n+1).
A054564: Prime number spiral (clockwise, Southeast spoke).
A081634: Class 6+ primes.
A158713: Primes p such that p1=Ceiling[p/2]+p is prime and p2=Ceiling[p1/2]+p is prime.
A227515: Values of n such that L(12) and N(12) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.
A236365: Primes whose binary and octal representation are also prime when read in decimal.
A291631: Numbers k such that 6 is the smallest decimal digit of k^2.

Number of the day: 27930

Luitzen Egbertus Jan Brouwer was born on this day 137 years ago.

Properties of the number 27930:

27930 = 2 × 3 × 5 × 7² × 19 is the 24882^th composite number and is not squarefree.
27930 has 5 distinct prime factors, 48 divisors, 27 antidivisors and 6048 totatives.
27930 has a semiprime digit sum 21 in base 10.
27930 has a Fibonacci digit sum 21 in base 10.
27930 has a triangular digit sum 21 in base 10.
27930 = (20 × 21)/2 + … + (55 × 56)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
27930 is the sum of 2 positive triangular numbers.
27930 is the difference of 2 positive pentagonal numbers in 5 ways.
27930 = 4² + 5² + 167² is the sum of 3 positive squares.
27930² = 16758² + 22344² is the sum of 2 positive squares in 1 way.
27930² is the sum of 3 positive squares.
27930 is a proper divisor of 1861² - 1.
27930 is palindromic in (at least) the following bases: 11, 47, 87, and -31.
27930 in base 30 = 1110 and consists of only the digits '0' and '1'.
27930 in base 47 = CUC and consists of only the digits 'C' and 'U'.

The number 27930 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002624: Expansion of (1-x)^(-3) * (1-x^2)^(-2).
A004320: a(n) = n*(n+1)*(n+2)^2/6.
A027444: a(n) = n^3 + n^2 + n.
A069070: Numbers n such that n*sigma(n) is a perfect square.
A091054: Expansion of (1-5x+2x^2)/((1-x)(1+2x)(1-6x)).
A132461: Row squared sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..floor(n/2)} A034807(n,k)^2, with a(0)=1.
A189507: Triangle read by rows: T(n,k) (n >= 0, 1 <= k <= n+1) are the signed Hultman numbers.
A203108: T(n,k)=Number of nXk binary arrays with every 1 immediately preceded by 0 0 to the left or above
A241649: Numbers m such that the GCD of the x's that satisfy sigma(x)=m is 4.
A255048: Partial sums of A253088.

Number of the day: 22009

Properties of the number 22009:

22009 is a cyclic number.
22009 = 13 × 1693 is semiprime and squarefree.
22009 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 20304 totatives.
22009 has an emirp digit sum 13 in base 10.
22009 has a Fibonacci digit sum 13 in base 10.
22009 = 11005² - 11004² = 853² - 840² is the difference of 2 nonnegative squares in 2 ways.
22009 is the sum of 2 positive triangular numbers.
22009 is the difference of 2 positive pentagonal numbers in 2 ways.
22009 = 75² + 128² = 20² + 147² is the sum of 2 positive squares in 2 ways.
22009 = 7² + 78² + 126² is the sum of 3 positive squares.
22009² = 8465² + 20316² = 5880² + 21209² = 10759² + 19200² = 13585² + 17316² is the sum of 2 positive squares in 4 ways.
22009² is the sum of 3 positive squares.
22009 is a proper divisor of 433⁶ - 1.
22009 is an emirpimes in (at least) the following bases: 2, 3, 4, 6, 7, 8, 9, 13, 15, 16, 17, 20, 23, 27, 28, 29, 31, 32, 33, 34, 37, 39, 40, 45, 46, 51, 56, 57, 67, 71, 73, 80, 82, 84, 85, 89, 95, 97, and 98.
22009 is palindromic in (at least) the following bases: -29, -50, and -57.
22009 in base 7 = 121111 and consists of only the digits '1' and '2'.
22009 in base 49 = 988 and consists of only the digits '8' and '9'.
22009 in base 56 = 711 and consists of only the digits '1' and '7'.
22009 in base 60 = 66n and consists of only the digits '6' and 'n'.

The number 22009 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A077416: Chebyshev S-sequence with Diophantine property.
A088669: Number of partitions of n into decimal repdigit numbers.
A091580: Number of partitions of n into decimal palindromes.
A099505: A transform of the Fibonacci numbers.
A120760: a(1) = a(2) = 1. a(n) = a(n-1) + (largest nonprime {1 or composite} among the first n-2 terms of the sequence).
A135859: Row sums of triangle A135858.
A151792: Partial sums of A151791.
A200669: Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its three previous neighbors modulo (n+1)
A288605: Position of first appearance of each integer in A088568 (number of 1's minus number of 2's in first n terms of A000002).
A297740: The number of distinct positions on an infinite chess board reachable by the (2,3)-leaper in <= n moves.

Number of the day: 992267

Properties of the number 992267:

992267 is a cyclic number.
992267 and 992269 form a twin prime pair.
992267 has 13 antidivisors and 992266 totatives.
992267 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 992267 results in a sphenic number.
992267 = 496134² - 496133² is the difference of 2 nonnegative squares in 1 way.
992267 is the difference of 2 positive pentagonal numbers in 1 way.
992267 = 17² + 77² + 993² is the sum of 3 positive squares.
992267² is the sum of 3 positive squares.
992267 is a proper divisor of 1439¹²¹⁹ - 1.
992267 is an emirp in (at least) the following bases: 2, 5, 15, 27, 35, 41, 50, 77, 82, 84, 86, 87, 88, 91, and 94.

The number 992267 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A188273: Number of nondecreasing strings of numbers x(i=1..n) in -5..5 with sum x(i)^3 equal to 0.

Number of the day: 112779

Properties of the number 112779:

112779 = 3³ × 4177 is the 102095^th composite number and is not squarefree.
112779 has 2 distinct prime factors, 8 divisors, 11 antidivisors and 75168 totatives.
112779 = 56390² - 56389² = 18798² - 18795² = 6270² - 6261² = 2102² - 2075² is the difference of 2 nonnegative squares in 4 ways.
112779 is the difference of 2 positive pentagonal numbers in 1 way.
112779 = 5² + 23² + 335² is the sum of 3 positive squares.
112779² = 31104² + 108405² is the sum of 2 positive squares in 1 way.
112779² is the sum of 3 positive squares.
112779 is a proper divisor of 151¹⁸ - 1.
112779 in base 51 = hII and consists of only the digits 'I' and 'h'.

Number of the day: 574421601

Properties of the number 574421601:

574421601 = 3 × 13 × 113 × 130343 is the 544364034^th composite number and is squarefree.
574421601 has 4 distinct prime factors, 16 divisors, 29 antidivisors and 350359296 totatives.
574421601 has a sphenic digit sum 30 in base 10.
574421601 has an oblong digit sum 30 in base 10.
574421601 = 287210801² - 287210800² = 95736935² - 95736932² = 22093145² - 22093132² = 7364399² - 7364360² = 2541745² - 2541632² = 847399² - 847060² = 196249² - 194780² = 67375² - 62968² is the difference of 2 nonnegative squares in 8 ways.
574421601 is the difference of 2 positive pentagonal numbers in 4 ways.
574421601 = 11² + 494² + 23962² is the sum of 3 positive squares.
574421601² = 148591020² + 554870151² = 76250655² + 569338224² = 289361460² + 496215801² = 220931385² + 530235324² is the sum of 2 positive squares in 4 ways.
574421601² is the sum of 3 positive squares.
574421601 is a proper divisor of 677¹³⁰³⁴² - 1.

Number of the day: 630919

Frank Plumpton Ramsey was born on this day 115 years ago.

Properties of the number 630919:

630919 is a cyclic number.
630919 is the 51405^th prime.
630919 has 3 antidivisors and 630918 totatives.
630919 has a triangular digit sum 28 in base 10.
630919 = 315460² - 315459² is the difference of 2 nonnegative squares in 1 way.
630919 is the sum of 2 positive triangular numbers.
630919 is the difference of 2 positive pentagonal numbers in 1 way.
630919 is not the sum of 3 positive squares.
630919² is the sum of 3 positive squares.
630919 is a proper divisor of 227³⁵⁰⁵¹ - 1.
630919 = '63091' + '9' is the concatenation of 2 semiprime numbers.
630919 is an emirp in (at least) the following bases: 9, 13, 14, 25, 30, 32, 36, 39, 51, 53, 63, 65, 67, 77, 82, 87, and 97.
630919 is palindromic in (at least) base -92.

Number of the day: 73348

Properties of the number 73348:

73348 = 2² × 11 × 1667 is the 66104^th composite number and is not squarefree.
73348 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 33320 totatives.
73348 has a semiprime digit sum 25 in base 10.
73348 has a triangular digit product 2016 in base 10.
73348 = 18338² - 18336² = 1678² - 1656² is the difference of 2 nonnegative squares in 2 ways.
73348 is the difference of 2 positive pentagonal numbers in 2 ways.
73348 = 104² + 126² + 216² is the sum of 3 positive squares.
73348² is the sum of 3 positive squares.
73348 is a proper divisor of 263³⁴ - 1.
73348 is palindromic in (at least) the following bases: 95, -52, and -74.
73348 in base 51 = SAA and consists of only the digits 'A' and 'S'.

The number 73348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A269652: Number of length-n 0..4 arrays with no adjacent pair x,x+1 repeated.
A269656: T(n,k)=Number of length-n 0..k arrays with no adjacent pair x,x+1 repeated.
A269660: Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated.

Number of the day: 99128

Properties of the number 99128:

99128 = 2³ × 12391 is the 89611^th composite number and is not squarefree.
99128 has 2 distinct prime factors, 8 divisors, 7 antidivisors and 49560 totatives.
99128 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 99128 results in a semiprime.
99128 = 4³ + 12³ + 46³ is the sum of 3 positive cubes in 1 way.
99128 = 24783² - 24781² = 12393² - 12389² is the difference of 2 nonnegative squares in 2 ways.
99128 is the sum of 2 positive triangular numbers.
99128 = 18² + 52² + 310² is the sum of 3 positive squares.
99128² is the sum of 3 positive squares.
99128 is a proper divisor of 1213⁷⁰ - 1.
99128 in base 26 = 5ggg and consists of only the digits '5' and 'g'.
99128 in base 59 = SS8 and consists of only the digits '8' and 'S'.

The number 99128 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058493: McKay-Thompson series of class 12e for Monster.
A112149: McKay-Thompson series of class 12f for the Monster group.
A252189: Number of (n+2)X(5+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 1 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 1 3 6 or 7

Number of the day: 6678446

Properties of the number 6678446:

6678446 = 2 × 59 × 56597 is a sphenic number and squarefree.
6678446 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 3282568 totatives.
6678446 has a prime digit sum 41 in base 10.
Reversing the decimal digits of 6678446 results in a sphenic number.
6678446 is the difference of 2 positive pentagonal numbers in 2 ways.
6678446 = 74² + 179² + 2577² is the sum of 3 positive squares.
6678446² = 3336450² + 5785304² is the sum of 2 positive squares in 1 way.
6678446² is the sum of 3 positive squares.
6678446 is a proper divisor of 1063¹⁴¹⁴⁹ - 1.
6678446 = '6' + '678446' is the concatenation of 2 semiprime numbers.
6678446 = '66' + '78446' is the concatenation of 2 sphenic numbers.

Number of the day: 28180

Properties of the number 28180:

28180 = 2² × 5 × 1409 is the 25108^th composite number and is not squarefree.
28180 has 3 distinct prime factors, 12 divisors, 5 antidivisors and 11264 totatives.
28180 has a prime digit sum 19 in base 10.
28180 = 7046² - 7044² = 1414² - 1404² is the difference of 2 nonnegative squares in 2 ways.
28180 is the difference of 2 positive pentagonal numbers in 2 ways.
28180 = 62² + 156² = 44² + 162² is the sum of 2 positive squares in 2 ways.
28180 = 60² + 62² + 144² is the sum of 3 positive squares.
28180² = 14256² + 24308² = 3180² + 28000² = 19344² + 20492² = 16908² + 22544² is the sum of 2 positive squares in 4 ways.
28180² is the sum of 3 positive squares.
28180 is a proper divisor of 1861⁴ - 1.
28180 is palindromic in (at least) base 43.
28180 in base 38 = JJM and consists of only the digits 'J' and 'M'.
28180 in base 42 = Fee and consists of only the digits 'F' and 'e'.
28180 in base 43 = FAF and consists of only the digits 'A' and 'F'.

The number 28180 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A293597: L.g.f.: Sum_{n>=1} (x - x^(2*n-1))^(2*n-1) / (2*n-1).

Number of the day: 896496

Properties of the number 896496:

896496 = 2⁴ × 3 × 19 × 983 is the 825465^th composite number and is not squarefree.
896496 has 4 distinct prime factors, 40 divisors, 9 antidivisors and 282816 totatives.
896496 has a sphenic digit sum 42 in base 10.
896496 has an oblong digit sum 42 in base 10.
Reversing the decimal digits of 896496 results in a sphenic number.
896496 is the difference of 2 nonnegative squares in 12 ways.
896496 is the difference of 2 positive pentagonal numbers in 1 way.
896496 is not the sum of 3 positive squares.
896496² is the sum of 3 positive squares.
896496 is a proper divisor of 113⁹⁸² - 1.
896496 in base 56 = 55mm and consists of only the digits '5' and 'm'.

The number 896496 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A025275: a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.

Number of the day: 89525093

Properties of the number 89525093:

89525093 = 7 × 19 × 673121 is a sphenic number and squarefree.
89525093 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 72696960 totatives.
89525093 has a prime digit sum 41 in base 10.
Reversing the decimal digits of 89525093 results in a sphenic number.
89525093 = 44762547² - 44762546² = 6394653² - 6394646² = 2355933² - 2355914² = 336627² - 336494² is the difference of 2 nonnegative squares in 4 ways.
89525093 is the difference of 2 positive pentagonal numbers in 4 ways.
89525093 = 2² + 183² + 9460² is the sum of 3 positive squares.
89525093² = 38959557² + 80603320² is the sum of 2 positive squares in 1 way.
89525093² is the sum of 3 positive squares.
89525093 is a proper divisor of 281⁵⁰⁴⁰ - 1.
89525093 = '8952509' + '3' is the concatenation of 2 prime numbers.
89525093 = '895' + '25093' is the concatenation of 2 semiprime numbers.

Number of the day: 494366

Galileo Galilei was born on this day 454 years ago.

Alfred North Whitehead was born on this day 157 years ago.

Properties of the number 494366:

494366 = 2 × 247183 is semiprime and squarefree.
494366 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 247182 totatives.
494366 = 6² + 11² + 703² is the sum of 3 positive squares.
494366² is the sum of 3 positive squares.
494366 is a proper divisor of 457³¹⁶⁹ - 1.
494366 = '494' + '366' is the concatenation of 2 sphenic numbers.
494366 is an emirpimes in (at least) the following bases: 3, 4, 7, 12, 25, 27, 31, 34, 36, 38, 39, 43, 44, 49, 50, 52, 53, 54, 55, 60, 63, 64, 66, 67, 69, 70, 73, 74, 75, 76, 78, 79, 80, 86, 89, 90, 91, 94, 95, and 100.

Number of the day: 73438635

Properties of the number 73438635:

73438635 is a cyclic number.
73438635 = 3 × 5 × 4895909 is a sphenic number and squarefree.
73438635 has 3 distinct prime factors, 8 divisors, 21 antidivisors and 39167264 totatives.
73438635 has an emirpimes digit sum 39 in base 10.
Reversing the decimal digits of 73438635 results in a sphenic number.
73438635 = 36719318² - 36719317² = 12239774² - 12239771² = 7343866² - 7343861² = 2447962² - 2447947² is the difference of 2 nonnegative squares in 4 ways.
73438635 is the sum of 2 positive triangular numbers.
73438635 is the difference of 2 positive pentagonal numbers in 2 ways.
73438635 = 43² + 95² + 8569² is the sum of 3 positive squares.
73438635² = 44063181² + 58750908² = 39549672² + 61879371² = 48330288² + 55293909² = 5487885² + 73233300² is the sum of 2 positive squares in 4 ways.
73438635² is the sum of 3 positive squares.
73438635 is a proper divisor of 61^1223977 - 1.
73438635 = '7343863' + '5' is the concatenation of 2 prime numbers.
73438635 = '734' + '38635' is the concatenation of 2 emirpimes.

Number of the day: 482394

Properties of the number 482394:

482394 = 2 × 3 × 11 × 7309 is the 442203^th composite number and is squarefree.
482394 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 146160 totatives.
482394 has a sphenic digit sum 30 in base 10.
482394 has an oblong digit sum 30 in base 10.
482394 is the sum of 2 positive triangular numbers.
482394 is the difference of 2 positive pentagonal numbers in 2 ways.
482394 = 28² + 83² + 689² is the sum of 3 positive squares.
482394² = 320694² + 360360² is the sum of 2 positive squares in 1 way.
482394² is the sum of 3 positive squares.
482394 is a proper divisor of 947³⁶ - 1.
482394 = '482' + '394' is the concatenation of 2 semiprime numbers.

Number of the day: 747250

Properties of the number 747250:

747250 = 2 × 5³ × 7² × 61 is the 687217^th composite number and is not squarefree.
747250 has 4 distinct prime factors, 48 divisors, 27 antidivisors and 252000 totatives.
747250 has a semiprime digit sum 25 in base 10.
747250 is the sum of 2 positive triangular numbers.
747250 is the difference of 2 positive pentagonal numbers in 13 ways.
747250 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
747250 = 455² + 735² = 77² + 861² = 315² + 805² = 231² + 833² is the sum of 2 positive squares in 4 ways.
747250 = 95² + 132² + 849² is the sum of 3 positive squares.
747250² = 333200² + 668850² = 134750² + 735000² = 335160² + 667870² = 507150² + 548800² = 132594² + 735392² = 76440² + 743330² = 384846² + 640528² = 448350² + 597800² = 209230² + 717360² = 263032² + 699426² is the sum of 2 positive squares in 10 ways.
747250² is the sum of 3 positive squares.
747250 is a proper divisor of 1451³⁰ - 1.
747250 is palindromic in (at least) base -96.

The number 747250 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A201236: Number of ways to place 2 non-attacking wazirs on an n X n toroidal board.

Number of the day: 758480

Properties of the number 758480:

758480 = 2⁴ × 5 × 19 × 499 is the 697620^th composite number and is not squarefree.
758480 has 4 distinct prime factors, 40 divisors, 27 antidivisors and 286848 totatives.
758480 is the difference of 2 nonnegative squares in 12 ways.
758480 is the difference of 2 positive pentagonal numbers in 4 ways.
758480 = 12² + 160² + 856² is the sum of 3 positive squares.
758480² = 455088² + 606784² is the sum of 2 positive squares in 1 way.
758480² is the sum of 3 positive squares.
758480 is a proper divisor of 359¹⁸ - 1.
758480 is palindromic in (at least) base 79.

Number of the day: 56177405379

Daniel Bernoulli was born on this day 318 years ago.

Properties of the number 56177405379:

56177405379 = 3² × 41 × 67 × 2272273 is composite and not squarefree.
56177405379 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 35992788480 totatives.
56177405379 = 1508³ + 2404³ + 3387³ is the sum of 3 positive cubes in 1 way.
56177405379 is the difference of 2 nonnegative squares in 12 ways.
56177405379 is the difference of 2 positive pentagonal numbers in 4 ways.
56177405379 = 223² + 3275² + 236995² is the sum of 3 positive squares.
56177405379² = 12331625571² + 54807224760² = 10062965304² + 55268776035² = 32765712696² + 45632323485² = 21949697475² + 51711813504² is the sum of 2 positive squares in 4 ways.
56177405379² is the sum of 3 positive squares.
56177405379 is a proper divisor of 163^1136136 - 1.
56177405379 = '56177' + '405379' is the concatenation of 2 semiprime numbers.

Number of the day: 99107

Properties of the number 99107:

99107 = 23 × 31 × 139 is a sphenic number and squarefree.
99107 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 91080 totatives.
99107 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 99107 results in a prime.
99107 = 27³ + 32³ + 36³ is the sum of 3 positive cubes in 1 way.
99107 = 49554² - 49553² = 2166² - 2143² = 1614² - 1583² = 426² - 287² is the difference of 2 nonnegative squares in 4 ways.
99107 is the difference of 2 positive pentagonal numbers in 3 ways.
99107 = 7² + 33² + 313² is the sum of 3 positive squares.
99107² is the sum of 3 positive squares.
99107 is a proper divisor of 277¹⁰ - 1.
99107 = '9' + '9107' is the concatenation of 2 semiprime numbers.
99107 is palindromic in (at least) base -87.

Number of the day: 8087872830

Properties of the number 8087872830:

8087872830 = 2 × 3 × 5 × 173 × 1558357 is the 7716235498^th composite number and is squarefree.
8087872830 has 5 distinct prime factors, 32 divisors, 23 antidivisors and 2144297856 totatives.
8087872830 has an emirpimes digit sum 51 in base 10.
8087872830 is the sum of 2 positive triangular numbers.
8087872830 is the difference of 2 positive pentagonal numbers in 4 ways.
8087872830 = 542² + 595² + 89929² is the sum of 3 positive squares.
8087872830² = 4852723698² + 6470298264² = 4712471568² + 6573149826² = 2683490754² + 7629715872² = 4725975384² + 6563447538² = 2534605008² + 7680459906² = 108820296² + 8087140722² = 2699171058² + 7624182744² = 282692034² + 8082930912² = 2159931918² + 7794124776² = 4939340670² + 6404420400² = 4623604920² + 6635959950² = 2415172800² + 7718848830² = 2431036920² + 7713867150² is the sum of 2 positive squares in 13 ways.
8087872830² is the sum of 3 positive squares.
8087872830 is a proper divisor of 467⁸⁷⁷² - 1.
8087872830 = '808787' + '2830' is the concatenation of 2 sphenic numbers.

Number of the day: 3733

Bartel Leendert van der Waerden was born on this day 115 years ago.

Properties of the number 3733:

3733 is a cyclic number.
3733 is the 521^th prime.
3733 has 9 antidivisors and 3732 totatives.
3733 has sum of divisors equal to 3734 which is semiprime.
Reversing the decimal digits of 3733 results in an emirp.
3733 = 1867² - 1866² is the difference of 2 nonnegative squares in 1 way.
3733 is the sum of 2 positive triangular numbers.
3733 is the difference of 2 positive pentagonal numbers in 1 way.
3733 = 22² + 57² is the sum of 2 positive squares in 1 way.
3733 = 23² + 30² + 48² is the sum of 3 positive squares.
3733² = 2508² + 2765² is the sum of 2 positive squares in 1 way.
3733² is the sum of 3 positive squares.
3733 is a proper divisor of 3³¹¹ - 1.
3733 = '3' + '733' is the concatenation of 2 prime numbers.
3733 is an emirp in (at least) the following bases: 2, 5, 8, 10, 14, 15, 18, 19, 21, 27, 29, 32, 37, 43, 45, 50, 55, 56, 59, 65, 67, 70, 71, 76, 77, 78, 79, 81, 82, 85, 89, 90, 91, 93, 94, 95, 97, and 99.
3733 is palindromic in (at least) the following bases: 23, 41, and -33.
3733 consists of only the digits '3' and '7'.
3733 in base 22 = 7ff and consists of only the digits '7' and 'f'.
3733 in base 23 = 717 and consists of only the digits '1' and '7'.
3733 in base 30 = 44d and consists of only the digits '4' and 'd'.
3733 in base 40 = 2DD and consists of only the digits '2' and 'D'.
3733 in base 41 = 292 and consists of only the digits '2' and '9'.

The number 3733 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006562: Balanced primes (of order one): primes which are the average of the previous prime and the following prime.
A019546: Primes whose digits are primes.
A024770: Right-truncatable primes: every prefix is prime.
A053445: Second differences of partition numbers A000041.
A069489: Primes > 1000 in which every substring of length 3 is also prime.
A081633: Class 5+ primes (for definition see A005105).
A133960: Home primes whose homeliness is 3.
A142199: Primes congruent to 2 mod 41.
A211685: Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).
A226929: Values of n such that L(9) and N(9) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.

Number of the day: 7269270

John Napier was born on this day 468 years ago.

John Napier was born on this day 468 years ago.

Properties of the number 7269270:

7269270 = 2 × 3 × 5 × 242309 is the 6775557^th composite number and is squarefree.
7269270 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1938464 totatives.
7269270 has a semiprime digit sum 33 in base 10.
7269270 is the difference of 2 positive pentagonal numbers in 2 ways.
7269270 = 11² + 130² + 2693² is the sum of 3 positive squares.
7269270² = 4880304² + 5387478² = 4361562² + 5815416² = 3176598² + 6538464² = 1381800² + 7136730² is the sum of 2 positive squares in 4 ways.
7269270² is the sum of 3 positive squares.
7269270 is a proper divisor of 599¹¹⁰¹⁴ - 1.