Number of the day: 57179507018

Properties of the number 57179507018:

57179507018 = 2 × 28589753509 is semiprime and squarefree.
57179507018 has 2 distinct prime factors, 4 divisors, 95 antidivisors and 28589753508 totatives.
57179507018 = 32837² + 236857² is the sum of 2 positive squares in 1 way.
57179507018 = 1917² + 2152² + 239105² is the sum of 3 positive squares.
57179507018² = 15555346618² + 55022969880² is the sum of 2 positive squares in 1 way.
57179507018² is the sum of 3 positive squares.
57179507018 is a proper divisor of 1093^18661719 - 1.
57179507018 is an emirpimes in (at least) the following bases: 11, 12, 16, 22, 26, 43, 44, 47, 57, 60, 72, 73, 74, 76, 78, 84, 85, and 87.

Number of the day: 33788

Properties of the number 33788:

33788 = 2² × 8447 is the 30169^th composite number and is not squarefree.
33788 has 2 distinct prime factors, 6 divisors, 23 antidivisors and 16892 totatives.
33788 has a prime digit sum 29 in base 10.
33788 has an oblong digit product 4032 in base 10.
Reversing the decimal digits of 33788 results in a semiprime.
33788 = 8448² - 8446² is the difference of 2 nonnegative squares in 1 way.
33788 is the sum of 2 positive triangular numbers.
33788 is the difference of 2 positive pentagonal numbers in 1 way.
33788 is not the sum of 3 positive squares.
33788² is the sum of 3 positive squares.
33788 is a proper divisor of 1789⁴¹ - 1.
33788 is palindromic in (at least) base -42.
33788 in base 41 = K44 and consists of only the digits '4' and 'K'.

The number 33788 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A204479: Number of (n+2)X6 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..3 introduced in row major order
A204482: Number of (n+2)X9 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..3 introduced in row major order

Number of the day: 6282018

Henri Léon Lebesgue was born on this day 143 years ago.

Happy τ Day!

Properties of the number 6282018:

6282018 = 2 × 3² × 263 × 1327 is the 5851123^th composite number and is not squarefree.
6282018 has 4 distinct prime factors, 24 divisors, 35 antidivisors and 2084472 totatives.
6282018 is the difference of 2 positive pentagonal numbers in 2 ways.
6282018 = 11² + 164² + 2501² is the sum of 3 positive squares.
6282018² is the sum of 3 positive squares.
6282018 is a proper divisor of 1051⁷⁸ - 1.

Number of the day: 466650

Properties of the number 466650:

466650 = 2 × 3² × 5² × 17 × 61 is the 427687^th composite number and is not squarefree.
466650 has 5 distinct prime factors, 72 divisors, 37 antidivisors and 115200 totatives.
466650 is the difference of 2 positive pentagonal numbers in 4 ways.
466650 = 225² + 645² = 105² + 675² = 477² + 489² = 381² + 567² = 321² + 603² = 207² + 651² is the sum of 2 positive squares in 6 ways.
466650 = 61² + 100² + 673² is the sum of 3 positive squares.
466650² = 219600² + 411750² = 141750² + 444600² = 290250² + 365400² = 71370² + 461160² = 12960² + 466470² = 153360² + 440730² = 197640² + 422730² = 118170² + 451440² = 270630² + 380160² = 326106² + 333792² = 260568² + 387126² = 269514² + 380952² = 95526² + 456768² = 11592² + 466506² = 176328² + 432054² = 279990² + 373320² = 208080² + 417690² = 316710² + 342720² = 84150² + 459000² = 130662² + 447984² = 47736² + 464202² = 209304² + 417078² is the sum of 2 positive squares in 22 ways.
466650² is the sum of 3 positive squares.
466650 is a proper divisor of 271¹⁰ - 1.
466650 = '46665' + '0' is the concatenation of 2 triangular numbers.
466650 is palindromic in (at least) base -82.

Number of the day: 7435

Properties of the number 7435:

7435 is a cyclic number.
7435 = 5 × 1487 is semiprime and squarefree.
7435 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 5944 totatives.
7435 has a prime digit sum 19 in base 10.
7435 has an oblong digit product 420 in base 10.
Reversing the decimal digits of 7435 results in a prime.
7435 = 4³ + 8³ + 19³ is the sum of 3 positive cubes in 1 way.
7435 = 3718² - 3717² = 746² - 741² is the difference of 2 nonnegative squares in 2 ways.
7435 is the sum of 2 positive triangular numbers.
7435 is the difference of 2 positive pentagonal numbers in 2 ways.
7435 = 21² + 55² + 63² is the sum of 3 positive squares.
7435² = 4461² + 5948² is the sum of 2 positive squares in 1 way.
7435² is the sum of 3 positive squares.
7435 is a proper divisor of 11⁷⁴³ - 1.
7435 = '743' + '5' is the concatenation of 2 prime numbers.
7435 = '74' + '35' is the concatenation of 2 semiprime numbers.
7435 is an emirpimes in (at least) the following bases: 6, 7, 8, 9, 18, 19, 20, 21, 28, 33, 36, 43, 49, 51, 52, 53, 64, 65, 66, 67, 70, 72, 73, 75, 77, 79, 80, 81, 86, 91, 95, 97, and 100.
7435 is palindromic in (at least) the following bases: 27, and 63.
7435 in base 9 = 11171 and consists of only the digits '1' and '7'.
7435 in base 26 = app and consists of only the digits 'a' and 'p'.
7435 in base 27 = a5a and consists of only the digits '5' and 'a'.
7435 in base 38 = 55P and consists of only the digits '5' and 'P'.
7435 in base 62 = 1vv and consists of only the digits '1' and 'v'.

The number 7435 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A051258: Fibocyclotomic numbers: numbers formed from cyclotomic polynomials and Fibonacci numbers (A000045).
A051673: Cubic star numbers: a(n) = n^3 + 4*Sum_{i=0..n-1} i^2.
A063704: Cyclotomic polynomials Phi_n at x=phi divided by sqrt(5) and floored down (where phi = tau = (sqrt(5)+1)/2).
A063706: Cyclotomic polynomials Phi_n at x=phi, divided by sqrt(5) and rounded to nearest integer (where phi = tau = (sqrt(5)+1)/2).
A122795: Connell (5,3)-sum sequence (partial sums of the (5,3)-Connell sequence)
A124502: a(1)=a(2)=1; thereafter, a(n+1) = a(n) + a(n-1) + 1 if n is a multiple of 5, otherwise a(n+1) = a(n) + a(n-1).
A138134: a(n) = sum(k=0..n, Fibonacci(5*k) ).
A157999: 338n - 1.
A158393: 676n - 1.
A158628: 44n^2-1.

Number of the day: 73871

Alan Turing was born on this day 106 years ago.

Properties of the number 73871:

73871 is a cyclic number.
73871 = 7 × 61 × 173 is a sphenic number and squarefree.
73871 has 3 distinct prime factors, 8 divisors, 21 antidivisors and 61920 totatives.
73871 has an emirpimes digit sum 26 in base 10.
73871 has a triangular digit product 1176 in base 10.
Reversing the decimal digits of 73871 results in a prime.
73871 = 49² + … + 69² is the sum of at least 2 consecutive positive squares in 1 way.
73871 = 36936² - 36935² = 5280² - 5273² = 636² - 575² = 300² - 127² is the difference of 2 nonnegative squares in 4 ways.
73871 is the difference of 2 positive pentagonal numbers in 4 ways.
73871 is not the sum of 3 positive squares.
73871² = 22204² + 70455² = 9135² + 73304² = 34545² + 65296² = 13321² + 72660² is the sum of 2 positive squares in 4 ways.
73871² is the sum of 3 positive squares.
73871 is a proper divisor of 599¹² - 1.
73871 is palindromic in (at least) the following bases: -43, -44, -47, and -66.
73871 in base 43 = dee and consists of only the digits 'd' and 'e'.
73871 in base 46 = Yff and consists of only the digits 'Y' and 'f'.

The number 73871 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A084251: G.f.: A(x) = exp(sum(n>=1, A084250(n)*x^n/n)), where A084250 lists the least distinct positive integers that allow A(x) to be an integer power series.

Number of the day: 788196

Hermann Minkowski was born on this day 154 years ago.

Properties of the number 788196:

788196 = 2² × 3 × 19 × 3457 is the 725120^th composite number and is not squarefree.
788196 has 4 distinct prime factors, 24 divisors, 21 antidivisors and 248832 totatives.
788196 has an emirpimes digit sum 39 in base 10.
788196 = (191 × 192)/2 + … + (226 × 227)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
788196 = 197050² - 197048² = 65686² - 65680² = 10390² - 10352² = 3514² - 3400² is the difference of 2 nonnegative squares in 4 ways.
788196 is the sum of 2 positive triangular numbers.
788196 is the difference of 2 positive pentagonal numbers in 2 ways.
788196 = 80² + 86² + 880² is the sum of 3 positive squares.
788196² = 94620² + 782496² is the sum of 2 positive squares in 1 way.
788196² is the sum of 3 positive squares.
788196 is a proper divisor of 257¹⁸ - 1.

Number of the day: 837333

Properties of the number 837333:

837333 = 3² × 7 × 13291 is the 770634^th composite number and is not squarefree.
837333 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 478440 totatives.
837333 = 418667² - 418666² = 139557² - 139554² = 59813² - 59806² = 46523² - 46514² = 19947² - 19926² = 6677² - 6614² is the difference of 2 nonnegative squares in 6 ways.
837333 is the difference of 2 positive pentagonal numbers in 2 ways.
837333 = 74² + 121² + 904² is the sum of 3 positive squares.
837333² is the sum of 3 positive squares.
837333 is a proper divisor of 331¹³²⁹ - 1.
837333 = '83' + '7333' is the concatenation of 2 prime numbers.
837333 = '8373' + '33' is the concatenation of 2 semiprime numbers.
837333 in base 40 = D3DD and consists of only the digits '3' and 'D'.

Number of the day: 5275112

Blaise Pascal was born on this day 395 years ago.

Properties of the number 5275112:

5275112 = 2³ × 727 × 907 is the 4908800^th composite number and is not squarefree.
5275112 has 3 distinct prime factors, 16 divisors, 51 antidivisors and 2631024 totatives.
5275112 has a prime digit sum 23 in base 10.
5275112 = 1318779² - 1318777² = 659391² - 659387² = 2541² - 1087² = 2361² - 547² is the difference of 2 nonnegative squares in 4 ways.
5275112 = 24² + 110² + 2294² is the sum of 3 positive squares.
5275112² is the sum of 3 positive squares.
5275112 is a proper divisor of 1453³⁰² - 1.

Number of the day: 34899248

Properties of the number 34899248:

34899248 = 2⁴ × 2181203 is the 32758270^th composite number and is not squarefree.
34899248 has 2 distinct prime factors, 10 divisors, 33 antidivisors and 17449616 totatives.
34899248 has a prime digit sum 47 in base 10.
Reversing the decimal digits of 34899248 results in a sphenic number.
34899248 = 8724813² - 8724811² = 4362408² - 4362404² = 2181207² - 2181199² is the difference of 2 nonnegative squares in 3 ways.
34899248 is the difference of 2 positive pentagonal numbers in 1 way.
34899248 = 132² + 268² + 5900² is the sum of 3 positive squares.
34899248² is the sum of 3 positive squares.
34899248 is a proper divisor of 199¹²⁸³⁰⁶ - 1.

Number of the day: 544828

Properties of the number 544828:

544828 = 2² × 136207 is the 499892^th composite number and is not squarefree.
544828 has 2 distinct prime factors, 6 divisors, 25 antidivisors and 272412 totatives.
544828 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 544828 results in a sphenic number.
544828 = 136208² - 136206² is the difference of 2 nonnegative squares in 1 way.
544828 is the difference of 2 positive pentagonal numbers in 1 way.
544828 is not the sum of 3 positive squares.
544828² is the sum of 3 positive squares.
544828 is a proper divisor of 1087²⁸² - 1.

The number 544828 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A152784: Partial sums of Prime Fibonacci numbers/A005478.

Number of the day: 6450399

Properties of the number 6450399:

6450399 = 3² × 163 × 4397 is the 6008804^th composite number and is not squarefree.
6450399 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 4272912 totatives.
6450399 has a triangular digit sum 36 in base 10.
6450399 = 3225200² - 3225199² = 1075068² - 1075065² = 358360² - 358351² = 19868² - 19705² = 6840² - 6351² = 2932² - 1465² is the difference of 2 nonnegative squares in 6 ways.
6450399 is the difference of 2 positive pentagonal numbers in 1 way.
6450399 is not the sum of 3 positive squares.
6450399² = 4467015² + 4653324² is the sum of 2 positive squares in 1 way.
6450399² is the sum of 3 positive squares.
6450399 is a proper divisor of 1933¹⁴¹³ - 1.

Number of the day: 253568

Properties of the number 253568:

253568 = 2⁷ × 7 × 283 is the 231246^th composite number and is not squarefree.
253568 has 3 distinct prime factors, 32 divisors, 9 antidivisors and 108288 totatives.
253568 has a prime digit sum 29 in base 10.
253568 is the difference of 2 nonnegative squares in 12 ways.
253568 is the sum of 2 positive triangular numbers.
253568 = 32² + 120² + 488² is the sum of 3 positive squares.
253568² is the sum of 3 positive squares.
253568 is a proper divisor of 1087⁶ - 1.
253568 is palindromic in (at least) base 81.

The number 253568 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A041518: Numerators of continued fraction convergents to sqrt(276).
A252760: Number of moduli m such that the multiplicative order of n mod m equals n.

Number of the day: 86203

Andrey Andreyevich Markov was born on this day 162 years ago.

Properties of the number 86203:

86203 is a cyclic number.
86203 = 13 × 19 × 349 is a sphenic number and squarefree.
86203 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 75168 totatives.
86203 has a prime digit sum 19 in base 10.
86203 = 48³ - 29³ is the difference of 2 positive cubes in 1 way.
86203 = 43102² - 43101² = 3322² - 3309² = 2278² - 2259² = 298² - 51² is the difference of 2 nonnegative squares in 4 ways.
86203 is the difference of 2 positive pentagonal numbers in 3 ways.
86203 = 1² + 39² + 291² is the sum of 3 positive squares.
86203² = 51072² + 69445² = 33155² + 79572² = 12635² + 85272² = 44460² + 73853² is the sum of 2 positive squares in 4 ways.
86203² is the sum of 3 positive squares.
86203 is a proper divisor of 911⁴ - 1.
86203 = '86' + '203' is the concatenation of 2 semiprime numbers.
86203 is palindromic in (at least) the following bases: -62, and -79.
86203 in base 18 = ee11 and consists of only the digits '1' and 'e'.
86203 in base 56 = RRJ and consists of only the digits 'J' and 'R'.
86203 in base 61 = NAA and consists of only the digits 'A' and 'N'.

The number 86203 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A123375: Least k such that the difference between consecutive semiprimes A065516(k) equals n, or 0 if no such k exists.
A125554: a(0)=2. a(n) = the a(n-1)th integer from among those positive integers coprime to n.
A228641: Volume of torus (rounded down) with major radius = n and minor radius = n/3.
A240707: Sum of the middle parts in the partitions of 4n-1 into 3 parts.

Number of the day: 27610

John Forbes Nash, Jr. was born on this day 90 years ago.

Properties of the number 27610:

27610 = 2 × 5 × 11 × 251 is the 24597^th composite number and is squarefree.
27610 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 10000 totatives.
27610 = 45² + … + 55² is the sum of at least 2 consecutive positive squares in 1 way.
27610 is the sum of 2 positive triangular numbers.
27610 is the difference of 2 positive pentagonal numbers in 3 ways.
27610 = 40² + 51² + 153² is the sum of 3 positive squares.
27610² = 16566² + 22088² is the sum of 2 positive squares in 1 way.
27610² is the sum of 3 positive squares.
27610 is a proper divisor of 149¹⁰ - 1.
27610 = '276' + '10' is the concatenation of 2 triangular numbers.
27610 is palindromic in (at least) the following bases: 32, 67, -41, -42, and -86.
27610 in base 32 = quq and consists of only the digits 'q' and 'u'.
27610 in base 40 = HAA and consists of only the digits 'A' and 'H'.
27610 in base 41 = GHH and consists of only the digits 'G' and 'H'.
27610 in base 52 = AAo and consists of only the digits 'A' and 'o'.

The number 27610 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A182724: Sum of all parts of all partitions of n minus the number of partitions of n.
A207255: Number of 4Xn 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically
A242691: Number of partitions of n with difference -1 between the number of odd parts and the number of even parts, both counted without multiplicity.
A248114: Number of subsets of {1,...,n} containing n and having at least one set partition into 5 blocks with equal element sum.

Number of the day: 658601

Vladimir Igorevich Arnold was born on this day 81 years ago.

Properties of the number 658601:

658601 is a cyclic number.
658601 is the 53460^th prime.
658601 has 9 antidivisors and 658600 totatives.
658601 has an emirpimes digit sum 26 in base 10.
658601 = 329301² - 329300² is the difference of 2 nonnegative squares in 1 way.
658601 is the difference of 2 positive pentagonal numbers in 1 way.
658601 = 499² + 640² is the sum of 2 positive squares in 1 way.
658601 = 51² + 56² + 808² is the sum of 3 positive squares.
658601² = 160599² + 638720² is the sum of 2 positive squares in 1 way.
658601² is the sum of 3 positive squares.
658601 is a proper divisor of 433⁹²⁵ - 1.
658601 is an emirp in (at least) the following bases: 7, 9, 17, 19, 37, 58, 67, 69, 70, 71, 77, 81, 82, 85, 89, 91, and 99.

Number of the day: 289511

Properties of the number 289511:

289511 is a cyclic number.
289511 is the 25188^th prime.
289511 has 7 antidivisors and 289510 totatives.
289511 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 289511 results in a semiprime.
289511 = 144756² - 144755² is the difference of 2 nonnegative squares in 1 way.
289511 is the difference of 2 positive pentagonal numbers in 1 way.
289511 is not the sum of 3 positive squares.
289511² is the sum of 3 positive squares.
289511 is a proper divisor of 1471¹³⁰ - 1.
289511 = '289' + '511' is the concatenation of 2 emirpimes.
289511 is an emirp in (at least) the following bases: 6, 7, 9, 11, 12, 17, 20, 22, 29, 31, 33, 34, 38, 39, 51, 53, 57, 58, 61, 64, 65, 67, 77, 84, 88, and 96.
289511 in base 13 = a1a11 and consists of only the digits '1' and 'a'.

Number of the day: 510964930593

John Edensor Littlewood was born on this day 133 years ago.

Properties of the number 510964930593:

510964930593 = 3³ × 13 × 37 × 2029 × 19391 is composite and not squarefree.
510964930593 has 5 distinct prime factors, 64 divisors, 69 antidivisors and 305775025920 totatives.
510964930593 is the difference of 2 nonnegative squares in 32 ways.
510964930593 is the difference of 2 positive pentagonal numbers in 6 ways.
510964930593 = 457² + 2920² + 714812² is the sum of 3 positive squares.
510964930593² = 303610180743² + 410981773860² = 153907433505² + 487234709568² = 12433955193² + 510813622620² = 207944275032² + 466737976575² = 45329565060² + 508950283257² = 122185638432² + 496140937695² = 350856487980² + 371463167943² = 237592784385² + 452365813368² = 78036694407² + 504970726500² = 338872791807² + 382426975080² = 196524973305² + 471659935932² = 32931211743² + 509902633440² = 165718355868² + 483345204615² is the sum of 2 positive squares in 13 ways.
510964930593² is the sum of 3 positive squares.
510964930593 is a proper divisor of 359¹¹⁶³⁴⁰ - 1.

Number of the day: 3457

Properties of the number 3457:

3457 is a cyclic number.
3457 is the 483^th prime.
3457 has 9 antidivisors and 3456 totatives.
3457 has a prime digit sum 19 in base 10.
3457 has an oblong digit product 420 in base 10.
Reversing the decimal digits of 3457 results in a semiprime.
3457 = 1³ + 12³ + 12³ = 9³ + 10³ + 12³ is the sum of 3 positive cubes in 2 ways.
3457 = 1729² - 1728² is the difference of 2 nonnegative squares in 1 way.
3457 is the sum of 2 positive triangular numbers.
3457 is the difference of 2 positive pentagonal numbers in 1 way.
3457 = 39² + 44² is the sum of 2 positive squares in 1 way.
3457 = 10² + 21² + 54² is the sum of 3 positive squares.
3457² = 415² + 3432² is the sum of 2 positive squares in 1 way.
3457² is the sum of 3 positive squares.
3457 is a proper divisor of 1741⁸ - 1.
3457 = '3' + '457' is the concatenation of 2 prime numbers.
3457 = '34' + '57' is the concatenation of 2 semiprime numbers.
3457 is an emirp in (at least) the following bases: 3, 4, 11, 16, 17, 31, 35, 41, 47, 50, 52, 56, 61, 62, 67, 71, 75, 76, 79, 83, 88, and 99.
3457 is palindromic in (at least) the following bases: 48, 54, -23, -64, -72, and -96.
3457 in base 22 = 733 and consists of only the digits '3' and '7'.
3457 in base 41 = 22D and consists of only the digits '2' and 'D'.
3457 in base 47 = 1QQ and consists of only the digits '1' and 'Q'.
3457 in base 48 = 1O1 and consists of only the digits '1' and 'O'.
3457 in base 53 = 1CC and consists of only the digits '1' and 'C'.
3457 in base 54 = 1A1 and consists of only the digits '1' and 'A'.
3457 in base 58 = 11Z and consists of only the digits '1' and 'Z'.

The number 3457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001126: Primes with 7 as smallest primitive root.
A002534: a(n) = 2*a(n-1) + 9*a(n-2).
A005109: Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1.
A022005: Initial members of prime triples (p, p+4, p+6).
A022007: Initial members of prime quintuplets (p, p+4, p+6, p+10, p+12).
A052378: Primes followed by a [4,2,4] prime difference pattern of A001223.
A058383: Primes of form 1+(2^a)*(3^b), a>0, b>0.
A086140: Primes p such that three (the maximum number) primes occur between p and p+12.
A128347: Numbers n such that (11^n - 5^n)/6 is prime.
A164294: Primes prime(k) such that all integers in [(prime(k-1)+1)/2,(prime(k)-1)/2] are composite, excluding those primes in A080359.

Number of the day: 5085

Properties of the number 5085:

5085 = 3² × 5 × 113 is the 4405^th composite number and is not squarefree.
5085 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 2688 totatives.
5085 = 2543² - 2542² = 849² - 846² = 511² - 506² = 287² - 278² = 177² - 162² = 79² - 34² is the difference of 2 nonnegative squares in 6 ways.
5085 is the sum of 2 positive triangular numbers.
5085 is the difference of 2 positive pentagonal numbers in 1 way.
5085 = 27² + 66² = 18² + 69² is the sum of 2 positive squares in 2 ways.
5085 = 10² + 19² + 68² is the sum of 3 positive squares.
5085² = 2484² + 4437² = 675² + 5040² = 3564² + 3627² = 3051² + 4068² is the sum of 2 positive squares in 4 ways.
5085² is the sum of 3 positive squares.
5085 is a proper divisor of 467⁴ - 1.
5085 is palindromic in (at least) the following bases: 62, -42, and -82.
5085 in base 21 = bb3 and consists of only the digits '3' and 'b'.
5085 in base 41 = 311 and consists of only the digits '1' and '3'.
5085 in base 61 = 1MM and consists of only the digits '1' and 'M'.
5085 in base 62 = 1K1 and consists of only the digits '1' and 'K'.

The number 5085 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024794: Number of 10's in all partitions of n.
A056108: Fourth spoke of a hexagonal spiral.
A067563: Product of n-th prime number and n-th composite number.
A100980: Number of totally ramified extensions over Q_3 with degree n in the algebraic closure of Q_3.
A137962: G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^3.
A180906: T(n,k)=number of sequences of n integers p(i) i=0..n-1 0<=p(i)<=k*i and |p(i+1)-p(i)|<=k
A205644: Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+287)^2 = y^2.
A211013: Second 13-gonal numbers: a(n) = n*(11*n+9)/2.
A231688: a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).
A252075: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 3 or 4

Number of the day: 601441

Aleksandr Mikhailovich Lyapunov was born on this day 161 years ago.

Properties of the number 601441:

601441 is a cyclic number.
601441 = 43 × 71 × 197 is a sphenic number and squarefree.
601441 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 576240 totatives.
Reversing the decimal digits of 601441 results in a semiprime.
601441 = 300721² - 300720² = 7015² - 6972² = 4271² - 4200² = 1625² - 1428² is the difference of 2 nonnegative squares in 4 ways.
601441 is the sum of 2 positive triangular numbers.
601441 is the difference of 2 positive pentagonal numbers in 4 ways.
601441 = 49² + 96² + 768² is the sum of 3 positive squares.
601441² = 85484² + 595335² is the sum of 2 positive squares in 1 way.
601441² is the sum of 3 positive squares.
601441 is a proper divisor of 1951¹⁴ - 1.
601441 is palindromic in (at least) base 70.

The number 601441 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A133343: a(n)=2a(n-1)+13a(n-2) for n>1, a(0)=1, a(1)=1 .
A221599: Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less
A298592: Triangle read by rows: T(n,k) = number of parking functions of length n whose lead number is k.

Number of the day: 1547

Properties of the number 1547:

1547 is a cyclic number.
1547 = 7 × 13 × 17 is a sphenic number and squarefree.
1547 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 1152 totatives.
1547 has an emirp digit sum 17 in base 10.
1547 has sum of divisors equal to 2016 which is a triangular number.
Reversing the decimal digits of 1547 results in a prime.
1547 = 11³ + 6³ is the sum of 2 positive cubes in 1 way.
1547 = 774² - 773² = 114² - 107² = 66² - 53² = 54² - 37² is the difference of 2 nonnegative squares in 4 ways.
1547 is the difference of 2 positive pentagonal numbers in 4 ways.
1547 = 1² + 5² + 39² is the sum of 3 positive squares.
1547² = 728² + 1365² = 147² + 1540² = 980² + 1197² = 595² + 1428² is the sum of 2 positive squares in 4 ways.
1547² is the sum of 3 positive squares.
1547 is a proper divisor of 883² - 1.
1547 is palindromic in (at least) the following bases: 14, 90, and -12.
1547 in base 14 = 7c7 and consists of only the digits '7' and 'c'.

The number 1547 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002412: Hexagonal pyramidal numbers, or greengrocer's numbers.
A002623: G.f.: 1/((1-x)^4*(1+x)).
A014377: Number of connected regular graphs of degree 7 with 2n nodes.
A018805: Number of elements in the set {(x,y): 1 <= x,y <= n, gcd(x,y)=1}.
A024670: Numbers that are sums of 2 distinct positive cubes.
A038812: Number of primes less than 1000n.
A050446: Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, read by upward antidiagonals.
A050447: Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, transposed and read by upward antidiagonals.
A068934: Triangular array C(n, r) = number of connected r-regular graphs with n nodes, 0 <= r < n.
A134600: Composite numbers such that the square mean of their prime factors is an integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).

Number of the day: 5727

Properties of the number 5727:

5727 is a cyclic number.
5727 = 3 × 23 × 83 is a sphenic number and squarefree.
5727 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 3608 totatives.
5727 has a semiprime digit sum 21 in base 10.
5727 has a Fibonacci digit sum 21 in base 10.
5727 has a triangular digit sum 21 in base 10.
5727 = 2864² - 2863² = 956² - 953² = 136² - 113² = 76² - 7² is the difference of 2 nonnegative squares in 4 ways.
5727 is the difference of 2 positive pentagonal numbers in 1 way.
5727 is not the sum of 3 positive squares.
5727² is the sum of 3 positive squares.
5727 is a proper divisor of 829² - 1.
5727 = '5' + '727' is the concatenation of 2 prime numbers.
5727 is palindromic in (at least) the following bases: 82, and -53.
5727 in base 12 = 3393 and consists of only the digits '3' and '9'.
5727 in base 53 = 223 and consists of only the digits '2' and '3'.

The number 5727 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000491: Number of bipartite partitions of n white objects and 5 black ones.
A007714: Number of 5-level rooted trees with n leaves.
A014160: Apply partial sum operator thrice to partition numbers.
A050341: Number of factorizations with 3 levels of parentheses indexed by prime signatures. A050340(A025487).
A086380: Numbers n such that p = n^2 + 2, p+2 and p+6 are consecutive primes.
A086381: Numbers n such that p=n^2+2 and p+2 are primes.
A098323: Recurrence sequence based on positions of digits in decimal places of 1/G, where G is Catalan's constant (also often called K).
A153692: Greatest number m such that the fractional part of (11/10^A153688(n) >= 1-(1/m).
A161804: G.f.: A(q) = exp( Sum_{n>=1} A002129(n) * 3*A038500(n) * q^n/n ).
A255528: G.f.: Product_{k>=1} 1/(1+x^k)^k.

Number of the day: 97311922797

Properties of the number 97311922797:

97311922797 is a cyclic number.
97311922797 = 3 × 149 × 217700051 is a sphenic number and squarefree.
97311922797 has 3 distinct prime factors, 8 divisors, 29 antidivisors and 64439214800 totatives.
97311922797 has a semiprime digit sum 57 in base 10.
Reversing the decimal digits of 97311922797 results in a sphenic number.
97311922797 = 48655961399² - 48655961398² = 16218653801² - 16218653798² = 326550151² - 326550002² = 108850249² - 108849802² is the difference of 2 nonnegative squares in 4 ways.
97311922797 is the difference of 2 positive pentagonal numbers in 2 ways.
97311922797 = 307² + 2552² + 311938² is the sum of 3 positive squares.
97311922797² = 33308107803² + 91434021420² is the sum of 2 positive squares in 1 way.
97311922797² is the sum of 3 positive squares.
97311922797 is a proper divisor of 701^17416004 - 1.
97311922797 = '97' + '311922797' is the concatenation of 2 prime numbers.
97311922797 = '9' + '7311922797' is the concatenation of 2 semiprime numbers.

Number of the day: 87752

Properties of the number 87752:

87752 = 2³ × 7 × 1567 is the 79228^th composite number and is not squarefree.
87752 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 37584 totatives.
87752 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 87752 results in a semiprime.
87752 = 21939² - 21937² = 10971² - 10967² = 3141² - 3127² = 1581² - 1553² is the difference of 2 nonnegative squares in 4 ways.
87752 = 40² + 66² + 286² is the sum of 3 positive squares.
87752² is the sum of 3 positive squares.
87752 is a proper divisor of 1031⁶ - 1.
87752 is palindromic in (at least) base 62.
87752 in base 24 = 6888 and consists of only the digits '6' and '8'.
87752 in base 62 = MpM and consists of only the digits 'M' and 'p'.

The number 87752 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A130281: Integers n > 1 such that A130280(4n^2) < n, i.e., there is an m < n, m > 1 such that 4n^2(m^2 - 1) + 1 is a square.
A222552: Number of (n+5)X1 arrays of occupancy after each element moves up to +-5 places but not 0
A222555: T(n,k)=Number of length (n+k)X1 arrays of occupancy after each element moves up to +-k places but not 0

Number of the day: 3200

Properties of the number 3200:

3200 = 2⁷ × 5² is the 2747^th composite number and is not squarefree.
3200 has 2 distinct prime factors, 24 divisors, 12 antidivisors and 1280 totatives.
3200 has a prime digit sum 5 in base 10.
3200 has a Fibonacci digit sum 5 in base 10.
3200 is the difference of 2 nonnegative squares in 9 ways.
3200 is the difference of 2 positive pentagonal numbers in 1 way.
3200 = 40² + 40² = 8² + 56² is the sum of 2 positive squares in 2 ways.
3200 = 24² + 32² + 40² is the sum of 3 positive squares.
3200² = 1920² + 2560² = 896² + 3072² is the sum of 2 positive squares in 2 ways.
3200² is the sum of 3 positive squares.
3200 is a proper divisor of 449² - 1.
3200 is palindromic in (at least) the following bases: 7, 19, 39, 63, 79, 99, -21, and -41.
3200 in base 7 = 12221 and consists of only the digits '1' and '2'.
3200 in base 19 = 8g8 and consists of only the digits '8' and 'g'.
3200 in base 20 = 800 and consists of only the digits '0' and '8'.
3200 in base 38 = 288 and consists of only the digits '2' and '8'.
3200 in base 39 = 242 and consists of only the digits '2' and '4'.
3200 in base 40 = 200 and consists of only the digits '0' and '2'.
3200 in base 56 = 118 and consists of only the digits '1' and '8'.

The number 3200 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001105: a(n) = 2*n^2.
A003592: Numbers of the form 2^i*5^j with i, j >= 0.
A032563: Numbers n such that A102489(n) is divisible by n.
A046312: Numbers that are divisible by exactly 9 primes with multiplicity.
A052486: Achilles numbers - powerful but imperfect: writing n=product(p_i^e_i) then none of the e_i=1 (i.e., powerful(1)) but the highest common factor of the e_i>1 is 1 (so not perfect powers).
A053191: a(n) = n^2 * phi(n).
A069540: Multiples of 5 with digit sum 5.
A077221: a(0) = 0 and then alternately even and odd numbers in increasing order such that the sum of any two successive terms is a square.
A121040: Multiples of 20 containing a 20 in their decimal representation.
A139098: a(n) = 8*n^2.