Number of the day: 99558

René Descartes was born on this day 421 years ago.

Properties of the number 99558:

99558 = 2 × 3² × 5531 is the 90006^th composite number and is not squarefree.
99558 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 33180 totatives.
99558 has a triangular digit sum 36 in base 10.
99558 is the difference of 2 positive pentagonal numbers in 2 ways.
99558 = 34² + 41² + 311² is the sum of 3 positive squares.
99558² is the sum of 3 positive squares.
99558 is a divisor of 239³⁰ - 1.
99558 = '995' + '58' is the concatenation of 2 semiprime numbers.
99558 is palindromic in (at least) the following bases: -58, and -94.
99558 in base 11 = 68888 and consists of only the digits '6' and '8'.
99558 in base 57 = Uaa and consists of only the digits 'U' and 'a'.

The number 99558 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A101277: Number of partitions of 2n in which all odd parts occur with multiplicity 2. There is no restriction on the even parts.

Number of the day: 3553

Stefan Banach was born on this day 125 years ago.

Properties of the number 3553:

3553 = 11 × 17 × 19 is a sphenic number and squarefree.
3553 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 2880 totatives.
3553 = 1777² - 1776² = 167² - 156² = 113² - 96² = 103² - 84² is the difference of 2 nonnegative squares in 4 ways.
3553 is the sum of 2 positive triangular numbers.
3553 is the difference of 2 positive pentagonal numbers in 4 ways.
3553 = 15² + 32² + 48² is the sum of 3 positive squares.
3553² = 1672² + 3135² is the sum of 2 positive squares in 1 way.
3553² is the sum of 3 positive squares.
3553 is a divisor of 647⁵ - 1.
3553 is a palindrome (in base 10).
3553 is palindromic in (at least) the following bases: 48, -53, -74, and -96.
3553 in base 3 = 11212121 and consists of only the digits '1' and '2'.
3553 in base 9 = 4777 and consists of only the digits '4' and '7'.
3553 consists of only the digits '3' and '5'.
3553 in base 22 = 77b and consists of only the digits '7' and 'b'.
3553 in base 47 = 1SS and consists of only the digits '1' and 'S'.
3553 in base 48 = 1Q1 and consists of only the digits '1' and 'Q'.
3553 in base 59 = 11D and consists of only the digits '1' and 'D'.

The number 3553 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000566: Heptagonal numbers (or 7-gonal numbers): n(5n-3)/2.
A023548: Convolution of natural numbers >= 2 and Fibonacci numbers.
A056524: Palindromes with even number of digits.
A059820: Expansion of series related to Liouville's Last Theorem: g.f. sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^3 *product_{i=1..t} (1-x^i) ).
A080859: a(n) = 6*n^2 + 4*n + 1.
A083832: Palindromes of the form 4n + 1 where n is also a palindrome. Palindromes arising in A083831.
A131423: a(n) = n*(n+2)*(2*n-1)/3. Also, row sums of triangle A131422.
A152942: Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 4.
A182269: Number of representations of n as a sum of products of pairs of positive integers, considered to be equivalent when terms or factors are reordered.
A255159: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 0 or 1 and no column sum 0 or 1

Number of the day: 594283018985498

Properties of the number 594283018985498:

594283018985498 = 2 × 3217 × 92366027197 is a sphenic number and squarefree.
594283018985498 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 297049143462336 totatives.
594283018985498 has a prime digit sum 83 in base 10.
Reversing the decimal digits of 594283018985498 results in a sphenic number.
594283018985498 is the sum of 2 positive triangular numbers.
594283018985498 = 10914593² + 21798043² = 3534863² + 24120277² is the sum of 2 positive squares in 2 ways.
594283018985498 = 5040² + 12503² + 24377917² is the sum of 3 positive squares.
594283018985498² = 186209910829152² + 564356426173670² = 170523749434102² + 569292506127960² = 356026338274200² + 475833535082998² = 340316102175370² + 487193244262152² is the sum of 2 positive squares in 4 ways.
594283018985498² is the sum of 3 positive squares.
594283018985498 is a divisor of 1423^61577351464 - 1.
594283018985498 = '594283018' + '985498' is the concatenation of 2 sphenic numbers.

Number of the day: 4990517757

Alexander Grothendieck was born on this day 89 years ago.

Properties of the number 4990517757:

4990517757 = 3³ × 184833991 is the 4755987537^th composite number and is not squarefree.
4990517757 has 2 distinct prime factors, 8 divisors, 43 antidivisors and 3327011820 totatives.
4990517757 = 2495258879² - 2495258878² = 831752961² - 831752958² = 277250991² - 277250982² = 92417009² - 92416982² is the difference of 2 nonnegative squares in 4 ways.
4990517757 is the sum of 2 positive triangular numbers.
4990517757 is the difference of 2 positive pentagonal numbers in 1 way.
4990517757 = 877² + 1922² + 70612² is the sum of 3 positive squares.
4990517757² is the sum of 3 positive squares.
4990517757 is a divisor of 1871^1120206 - 1.

Number of the day: 980019

Properties of the number 980019:

980019 = 3⁵ × 37 × 109 is the 902951^th composite number and is not squarefree.
980019 has 3 distinct prime factors, 24 divisors, 35 antidivisors and 629856 totatives.
980019 = 195³ - 186³ is the difference of 2 positive cubes in 1 way.
980019 is the difference of 2 nonnegative squares in 12 ways.
980019 is the difference of 2 positive pentagonal numbers in 1 way.
980019 = 53² + 137² + 979² is the sum of 3 positive squares.
980019² = 598995² + 775656² = 317844² + 927045² = 244944² + 948915² = 539460² + 818181² is the sum of 2 positive squares in 4 ways.
980019² is the sum of 3 positive squares.
980019 is a divisor of 1619¹⁸ - 1.

Number of the day: 806475

Paul Erös was born on this day 104 years ago.

Properties of the number 806475:

806475 = 3 × 5² × 10753 is the 742039^th composite number and is not squarefree.
806475 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 430080 totatives.
806475 has a sphenic digit sum 30 in base 10.
806475 has an oblong digit sum 30 in base 10.
806475 = 403238² - 403237² = 134414² - 134411² = 80650² - 80645² = 26890² - 26875² = 16142² - 16117² = 5414² - 5339² is the difference of 2 nonnegative squares in 6 ways.
806475 is the difference of 2 positive pentagonal numbers in 3 ways.
806475 = 1² + 95² + 893² is the sum of 3 positive squares.
806475² = 322605² + 739140² = 185400² + 784875² = 397749² + 701568² = 516660² + 619245² = 41781² + 805392² = 483885² + 645180² = 225813² + 774216² is the sum of 2 positive squares in 7 ways.
806475² is the sum of 3 positive squares.
806475 is a divisor of 1499²⁸ - 1.

Number of the day: 4035901728

Properties of the number 4035901728:

4035901728 = 2⁵ × 3 × 17 × 2472979 is the 3844316984^th composite number and is not squarefree.
4035901728 has 4 distinct prime factors, 48 divisors, 19 antidivisors and 1266164736 totatives.
4035901728 has an emirpimes digit sum 39 in base 10.
4035901728 is the difference of 2 nonnegative squares in 16 ways.
4035901728 is the difference of 2 positive pentagonal numbers in 2 ways.
4035901728 = 640² + 1492² + 63508² is the sum of 3 positive squares.
4035901728² = 1899247872² + 3561089760² is the sum of 2 positive squares in 1 way.
4035901728² is the sum of 3 positive squares.
4035901728 is a divisor of 199³⁰⁷⁶⁸ - 1.

Number of the day: 569581

Joseph Liouville was born on this day 208 years ago.

Properties of the number 569581:

569579 and 569581 form a twin prime pair.
569581 has 5 antidivisors and 569580 totatives.
569581 has a semiprime digit sum 34 in base 10.
569581 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 569581 results in a sphenic number.
569581 = 284791² - 284790² is the difference of 2 nonnegative squares in 1 way.
569581 is the difference of 2 positive pentagonal numbers in 1 way.
569581 = 355² + 666² is the sum of 2 positive squares in 1 way.
569581 = 59² + 174² + 732² is the sum of 3 positive squares.
569581² = 317531² + 472860² is the sum of 2 positive squares in 1 way.
569581² is the sum of 3 positive squares.
569581 is a divisor of 1031¹⁷²⁶ - 1.
569581 is an emirp in (at least) the following bases: 9, 15, 19, 27, 48, 49, 56, 59, 61, 63, 66, 67, 71, 73, 76, 80, 81, 93, 96, and 97.

Number of the day: 1134

Pierre-Simon Laplace was born on this day 268 years ago.

Emmy Noether was born on this day 135 years ago.

Properties of the number 1134:

1134 = 2 × 3⁴ × 7 is the 944^th composite number and is not squarefree.
1134 has 3 distinct prime factors, 20 divisors, 9 antidivisors and 324 totatives.
1134 has a semiprime digit sum 9 in base 10.
1134 has an oblong digit product 12 in base 10.
1134 is the sum of 2 positive triangular numbers.
1134 = 2² + 13² + 31² is the sum of 3 positive squares.
1134² is the sum of 3 positive squares.
1134 is a divisor of 811² - 1.
1134 is palindromic in (at least) the following bases: 41, 53, 62, and 80.
1134 in base 33 = 11c and consists of only the digits '1' and 'c'.

The number 1134 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000969: G.f.: (1+x+2*x^2)/((1-x)^2*(1-x^3)).
A001158: sigma_3(n): sum of cubes of divisors of n.
A008290: Triangle T(n,k) of rencontres numbers (number of permutations of n elements with k fixed points).
A033485: a(n) = a(n-1) + a(floor(n/2)), a(1) = 1.
A045943: Triangular matchstick numbers: 3*n*(n+1)/2.
A046306: Numbers that are divisible by exactly 6 primes with multiplicity.
A057809: Numbers n such that pi(n) divides n.
A085787: Generalized heptagonal numbers: n*(5*n-3)/2, n=0, +-1, +-2 +-3, ...
A094159: 3 times hexagonal numbers: a(n) = 3*n*(2*n-1).
A179644: Product of the 4th power of a prime and 2 different distinct primes (p^4*q*r).

Number of the day: 9912

Properties of the number 9912:

9912 = 2³ × 3 × 7 × 59 is the 8689^th composite number and is not squarefree.
9912 has 4 distinct prime factors, 32 divisors, 19 antidivisors and 2784 totatives.
9912 has a semiprime digit sum 21 in base 10.
9912 has a Fibonacci digit sum 21 in base 10.
9912 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 9912 results in a semiprime.
9912 = 2479² - 2477² = 1241² - 1237² = 829² - 823² = 419² - 407² = 361² - 347² = 191² - 163² = 139² - 97² = 101² - 17² is the difference of 2 nonnegative squares in 8 ways.
9912 is the difference of 2 positive pentagonal numbers in 3 ways.
9912 = 20² + 26² + 94² is the sum of 3 positive squares.
9912² is the sum of 3 positive squares.
9912 is a divisor of 827² - 1.
9912 = '991' + '2' is the concatenation of 2 prime numbers.
9912 is palindromic in (at least) base 39.
9912 in base 38 = 6WW and consists of only the digits '6' and 'W'.
9912 in base 39 = 6K6 and consists of only the digits '6' and 'K'.
9912 in base 44 = 55C and consists of only the digits '5' and 'C'.

The number 9912 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002597: Number of partitions into one kind of 1's, two kinds of 2's, and three kinds of 3's.
A006967: Number of graceful permutations of length n.
A025231: a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3.
A047891: Number of planar rooted trees with n nodes and tricolored end nodes.
A049374: A triangle of numbers related to triangle A030527.
A092000: Numbers that can be expressed as the difference of the squares of primes in exactly four distinct ways.
A105720: Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.
A180281: Triangle read by rows: T(n,k) = number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to k.
A235047: Permutation of nonnegative integers: a(n) = A235199(A234840(n+1)-1).
A241648: Numbers m such that the GCD of the x's that satisfy sigma(x)=m is 3.

Number of the day: 1537116005136

Joseph Fourier was born on this day 249 years ago.

George David Birkhoff was born on this day 133 years ago.

Properties of the number 1537116005136:

1537116005136 = 2⁴ × 3 × 73 × 438674659 is composite and not squarefree.
1537116005136 has 4 distinct prime factors, 40 divisors, 35 antidivisors and 505353206016 totatives.
1537116005136 has an emirpimes digit sum 39 in base 10.
1537116005136 is the difference of 2 nonnegative squares in 12 ways.
1537116005136 is the difference of 2 positive pentagonal numbers in 2 ways.
1537116005136 = 2984² + 16756² + 1239688² is the sum of 3 positive squares.
1537116005136² = 1010706414336² + 1158101099760² is the sum of 2 positive squares in 1 way.
1537116005136² is the sum of 3 positive squares.
1537116005136 is a divisor of 439^146224886 - 1.
1537116005136 = '153711600513' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 689804

Properties of the number 689804:

689804 = 2² × 331 × 521 is the 634008^th composite number and is not squarefree.
689804 has 3 distinct prime factors, 12 divisors, 39 antidivisors and 343200 totatives.
689804 has a semiprime digit sum 35 in base 10.
689804 = 172452² - 172450² = 852² - 190² is the difference of 2 nonnegative squares in 2 ways.
689804 is the difference of 2 positive pentagonal numbers in 2 ways.
689804 = 2² + 30² + 830² is the sum of 3 positive squares.
689804² = 369396² + 582560² is the sum of 2 positive squares in 1 way.
689804² is the sum of 3 positive squares.
689804 is a divisor of 1667¹¹⁰ - 1.
689804 is palindromic in (at least) base -99.

Number of the day: 282

Properties of the number 282:

282 = 2 × 3 × 47 is a sphenic number and squarefree.
282 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 92 totatives.
282 has an oblong digit sum 12 in base 10.
282 = (3 × 4)/2 + … + (11 × 12)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
282 is the sum of 2 positive triangular numbers.
282 is the difference of 2 positive pentagonal numbers in 2 ways.
282 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
282 = 7² + 8² + 13² is the sum of 3 positive squares.
282² is the sum of 3 positive squares.
282 is a divisor of 281² - 1.
282 is a palindrome (in base 10).
282 is palindromic in (at least) the following bases: 5, 9, 46, 93, and -14.
282 in base 3 = 101110 and consists of only the digits '0' and '1'.
282 in base 5 = 2112 and consists of only the digits '1' and '2'.
282 in base 7 = 552 and consists of only the digits '2' and '5'.
282 in base 9 = 343 and consists of only the digits '3' and '4'.
282 consists of only the digits '2' and '8'.
282 in base 16 = 11a and consists of only the digits '1' and 'a'.

The number 282 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000219: Number of planar partitions of n.
A002113: Palindromes in base 10.
A002445: Denominators of Bernoulli numbers B_{2n}.
A002858: Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.
A005836: Numbers n whose base 3 representation contains no 2.
A007304: Sphenic numbers: products of 3 distinct primes.
A008864: a(n) = prime(n) + 1.
A014574: Average of twin prime pairs.
A024675: Average of two consecutive odd primes.
A027642: Denominator of Bernoulli number B_n.

Number of the day: 99300

Christian Goldbach was born on this day 327 years ago.

Properties of the number 99300:

99300 = 2² × 3 × 5² × 331 is the 89767^th composite number and is not squarefree.
99300 has 4 distinct prime factors, 36 divisors, 13 antidivisors and 26400 totatives.
99300 has a semiprime digit sum 21 in base 10.
99300 has a Fibonacci digit sum 21 in base 10.
99300 has a triangular digit sum 21 in base 10.
99300 = 24826² - 24824² = 8278² - 8272² = 4970² - 4960² = 1670² - 1640² = 1018² - 968² = 406² - 256² is the difference of 2 nonnegative squares in 6 ways.
99300 is the difference of 2 positive pentagonal numbers in 3 ways.
99300 = 44² + 50² + 308² is the sum of 3 positive squares.
99300² = 59580² + 79440² = 27804² + 95328² is the sum of 2 positive squares in 2 ways.
99300² is the sum of 3 positive squares.
99300 is a divisor of 181¹⁰ - 1.
99300 is palindromic in (at least) base 29.
99300 in base 29 = 4224 and consists of only the digits '2' and '4'.
99300 in base 47 = iia and consists of only the digits 'a' and 'i'.

Number of the day: 381096

Properties of the number 381096:

381096 = 2³ × 3² × 67 × 79 is the 348715^th composite number and is not squarefree.
381096 has 4 distinct prime factors, 48 divisors, 19 antidivisors and 123552 totatives.
381096 is the difference of 2 nonnegative squares in 12 ways.
381096 is the sum of 2 positive triangular numbers.
381096 = 14² + 136² + 602² is the sum of 3 positive squares.
381096² is the sum of 3 positive squares.
381096 is a divisor of 1579⁶ - 1.
381096 = '38109' + '6' is the concatenation of 2 semiprime numbers.
381096 is palindromic in (at least) base -74.

The number 381096 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A216507: E.g.f. exp( x^2 * exp(x) ).

Number of the day: 17813783

Properties of the number 17813783:

17813783 = 13² × 105407 is the 16673617^th composite number and is not squarefree.
17813783 has 2 distinct prime factors, 6 divisors, 37 antidivisors and 16443336 totatives.
17813783 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 17813783 results in a prime.
17813783 = 8906892² - 8906891² = 685152² - 685139² = 52788² - 52619² is the difference of 2 nonnegative squares in 3 ways.
17813783 is the difference of 2 positive pentagonal numbers in 3 ways.
17813783 is not the sum of 3 positive squares.
17813783² = 6851455² + 16443492² = 12543433² + 12648840² is the sum of 2 positive squares in 2 ways.
17813783² is the sum of 3 positive squares.
17813783 is a divisor of 337¹⁵⁰⁵⁸ - 1.

Number of the day: 9034526127028

Properties of the number 9034526127028:

9034526127028 = 2² × 350111 × 6451187 is composite and not squarefree.
9034526127028 has 3 distinct prime factors, 12 divisors, 63 antidivisors and 4517249460920 totatives.
9034526127028 has an emirpimes digit sum 49 in base 10.
Reversing the decimal digits of 9034526127028 results in a prime.
9034526127028 = 2258631531758² - 2258631531756² = 6801298² - 6101076² is the difference of 2 nonnegative squares in 2 ways.
9034526127028 is the difference of 2 positive pentagonal numbers in 1 way.
9034526127028 = 4746² + 7396² + 3005736² is the sum of 3 positive squares.
9034526127028² is the sum of 3 positive squares.
9034526127028 is a divisor of 1181^719307239 - 1.

Number of the day: 3142017

Albert Einstein was born on this day 138 years ago.

Happy π Day!

Properties of the number 3142017:

3142017 = 3³ × 116371 is the 2915717^th composite number and is not squarefree.
3142017 has 2 distinct prime factors, 8 divisors, 19 antidivisors and 2094660 totatives.
3142017 = 1571009² - 1571008² = 523671² - 523668² = 174561² - 174552² = 58199² - 58172² is the difference of 2 nonnegative squares in 4 ways.
3142017 is the sum of 2 positive triangular numbers.
3142017 is the difference of 2 positive pentagonal numbers in 1 way.
3142017 = 8² + 127² + 1768² is the sum of 3 positive squares.
3142017² is the sum of 3 positive squares.
3142017 is a divisor of 73¹²⁹³ - 1.
3142017 = '31' + '42017' is the concatenation of 2 prime numbers.

Number of the day: 426

Properties of the number 426:

426 = 2 × 3 × 71 is a sphenic number and squarefree.
426 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 140 totatives.
426 has an oblong digit sum 12 in base 10.
426 is the difference of 2 positive pentagonal numbers in 2 ways.
426 = 4² + 11² + 17² is the sum of 3 positive squares.
426² is the sum of 3 positive squares.
426 is a divisor of 283² - 1.
426 = '4' + '26' is the concatenation of 2 semiprime numbers.
426 = '42' + '6' is the concatenation of 2 oblong numbers.
426 is palindromic in (at least) the following bases: 17, 70, -4, -25, and -85.
426 in base 4 = 12222 and consists of only the digits '1' and '2'.
426 in base 14 = 226 and consists of only the digits '2' and '6'.
426 in base 16 = 1aa and consists of only the digits '1' and 'a'.
426 in base 17 = 181 and consists of only the digits '1' and '8'.
426 in base 20 = 116 and consists of only the digits '1' and '6'.

The number 426 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005114: Untouchable numbers, also called nonaliquot numbers: impossible values for sum of aliquot parts of n (A001065).
A006314: Numbers n such that n^8 + 1 is prime.
A007304: Sphenic numbers: products of 3 distinct primes.
A007588: Stella octangula numbers: a(n) = n*(2*n^2 - 1).
A074664: Number of algebraically independent elements of degree n in the algebra of symmetric polynomials in noncommuting variables.
A145271: Coefficients for expansion of (g(x)d/dx)^n g(x); refined Eulerian numbers for calculating compositional inverse of h(x)= (d/dx)^(-1) 1/g(x); iterated derivatives as infinitesimal generators of flows.
A163334: Hilbert II curve in N x N grid, starting rightwards from the top-left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
A235151: Numbers whose sum of digits is 12.
A255411: Shift factorial base representation of n one digit left (with 0 added to right), increment all nonzero digits by one, then convert back to decimal; Numbers with no digit 1 in their factorial base representation.
A259934: Infinite sequence starting with a(0)=0 such that A049820(a(k)) = a(k-1) for all k>=1, where A049820(n) = n - (number of divisors of n).

Number of the day: 9144

Properties of the number 9144:

9144 = 2³ × 3² × 127 is the 8010^th composite number and is not squarefree.
9144 has 3 distinct prime factors, 24 divisors, 5 antidivisors and 3024 totatives.
9144 has a Fibonacci digit product 144 in base 10.
9144 = 2287² - 2285² = 1145² - 1141² = 765² - 759² = 387² - 375² = 263² - 245² = 145² - 109² is the difference of 2 nonnegative squares in 6 ways.
9144 = 20² + 62² + 70² is the sum of 3 positive squares.
9144² is the sum of 3 positive squares.
9144 is a divisor of 19⁶ - 1.
9144 = '914' + '4' is the concatenation of 2 semiprime numbers.
9144 in base 26 = ddi and consists of only the digits 'd' and 'i'.

The number 9144 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A042092: Numerators of continued fraction convergents to sqrt(570).
A055302: Triangle of labeled rooted trees with n nodes and k leaves, n>=1, 1<=k<=n.
A071223: Triangle T(n,k) (n >= 2, 1 <= k <= n) read by rows: number of linearly inducible orderings of n points in k-dimensional Euclidean space.
A095066: Number of fib001 primes (A095086) in range ]2^n,2^(n+1)].
A100250: Positions where values change in A100144.
A101976: Number of products of factorials not exceeding n!.
A200534: T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards
A205926: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the number of clockwise edge increases in every 2X2 subblock equal to one, and every 2X2 determinant nonzero
A213493: Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y|,|y-w| distinct.
A262876: Expansion of Product_{k>=1} 1/(1-x^(3k-1))^k.

Number of the day: 627450

Properties of the number 627450:

627450 = 2 × 3 × 5² × 47 × 89 is the 576291^th composite number and is not squarefree.
627450 has 5 distinct prime factors, 48 divisors, 25 antidivisors and 161920 totatives.
627450 is the difference of 2 positive pentagonal numbers in 5 ways.
627450 = 41² + 80² + 787² is the sum of 3 positive squares.
627450² = 274950² + 564000² = 118440² + 616170² = 286230² + 558360² = 421872² + 464454² = 106032² + 618426² = 376470² + 501960² = 175686² + 602352² is the sum of 2 positive squares in 7 ways.
627450² is the sum of 3 positive squares.
627450 is a divisor of 751²² - 1.
627450 is palindromic in (at least) the following bases: 49, 93, and -95.
627450 in base 49 = 5GG5 and consists of only the digits '5' and 'G'.

Number of the day: 3829

Properties of the number 3829:

3829 = 7 × 547 is semiprime and squarefree.
3829 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 3276 totatives.
3829 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 3829 results in a prime.
3829 = 1915² - 1914² = 277² - 270² is the difference of 2 nonnegative squares in 2 ways.
3829 is the sum of 2 positive triangular numbers.
3829 is the difference of 2 positive pentagonal numbers in 2 ways.
3829 = 2² + 15² + 60² is the sum of 3 positive squares.
3829² is the sum of 3 positive squares.
3829 is a divisor of 1093² - 1.
3829 = '3' + '829' is the concatenation of 2 prime numbers.
3829 = '382' + '9' is the concatenation of 2 semiprime numbers.
3829 is an emirpimes in (at least) the following bases: 2, 5, 9, 11, 12, 14, 15, 23, 25, 31, 34, 39, 41, 48, 51, 54, 57, 60, 61, 63, 65, 71, 72, 73, 74, 80, 81, 83, 89, 91, 93, 97, and 99.
3829 is palindromic in (at least) the following bases: 19, 20, 43, 44, 58, -66, and -87.
3829 in base 17 = d44 and consists of only the digits '4' and 'd'.
3829 in base 19 = aba and consists of only the digits 'a' and 'b'.
3829 in base 20 = 9b9 and consists of only the digits '9' and 'b'.
3829 in base 42 = 277 and consists of only the digits '2' and '7'.
3829 in base 43 = 232 and consists of only the digits '2' and '3'.
3829 in base 44 = 1h1 and consists of only the digits '1' and 'h'.
3829 in base 57 = 1AA and consists of only the digits '1' and 'A'.
3829 in base 58 = 181 and consists of only the digits '1' and '8'.
3829 in base 61 = 11l and consists of only the digits '1' and 'l'.

The number 3829 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008987: Number of immersions of unoriented circle into oriented sphere with n double points.
A036437: Triangle of coefficients of generating function of ternary rooted trees of height exactly n.
A038764: a(n)=C(n,0)+6C(n,1)+9C(n,2).
A046254: a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A048268: Smallest palindrome greater than n in bases n and n+1.
A071148: Partial sums of sequence of odd primes (A065091); a(n) = sum of the first n odd primes.
A130883: a(n) = 2*n^2 - n + 1.
A263478: Total number of n-digit positive integers with multiplicative digital root value 4.
A266781: Molien series for invariants of finite Coxeter group A_12.
A275189: Positions of 4 in A274640.

Number of the day: 86127

Properties of the number 86127:

86127 = 3 × 19 × 1511 is a sphenic number and squarefree.
86127 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 54360 totatives.
86127 = 43064² - 43063² = 14356² - 14353² = 2276² - 2257² = 784² - 727² is the difference of 2 nonnegative squares in 4 ways.
86127 is the difference of 2 positive pentagonal numbers in 2 ways.
86127 is not the sum of 3 positive squares.
86127² is the sum of 3 positive squares.
86127 is a divisor of 977³⁰ - 1.
86127 is palindromic in (at least) the following bases: 45, 93, and -78.
86127 in base 21 = 9666 and consists of only the digits '6' and '9'.
86127 in base 45 = gNg and consists of only the digits 'N' and 'g'.

The number 86127 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A183629: Number of (n+1)X7 0..2 arrays with every 2x2 subblock summing to 4
A183631: Number of (n+1)X9 0..2 arrays with every 2x2 subblock summing to 4

Number of the day: 5463

Properties of the number 5463:

5463 = 3² × 607 is the 4741^th composite number and is not squarefree.
5463 has 2 distinct prime factors, 6 divisors, 19 antidivisors and 3636 totatives.
5463 = 2732² - 2731² = 912² - 909² = 308² - 299² is the difference of 2 nonnegative squares in 3 ways.
5463 is the sum of 2 positive triangular numbers.
5463 is the difference of 2 positive pentagonal numbers in 1 way.
5463 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
5463 is not the sum of 3 positive squares.
5463² is the sum of 3 positive squares.
5463 is a divisor of 211⁶ - 1.
5463 = '5' + '463' is the concatenation of 2 prime numbers.
5463 is palindromic in (at least) the following bases: 39, 42, 43, -2, and -52.
5463 in base 4 = 1111113 and consists of only the digits '1' and '3'.
5463 in base 20 = dd3 and consists of only the digits '3' and 'd'.
5463 in base 38 = 3TT and consists of only the digits '3' and 'T'.
5463 in base 39 = 3N3 and consists of only the digits '3' and 'N'.
5463 in base 41 = 3AA and consists of only the digits '3' and 'A'.
5463 in base 42 = 343 and consists of only the digits '3' and '4'.
5463 in base 43 = 2f2 and consists of only the digits '2' and 'f'.

The number 5463 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.
A023105: Number of distinct quadratic residues mod 2^n.
A090832: Numbers n such that p(n), p(n)+6, p(n)+12, p(n)+18 are consecutive primes, where p(n) denotes n-th prime.
A090838: Numbers n such that p(n),p(n)+6,p(n)+12,p(n)+18 are consecutive primes and p(n)=6*k+1 for some k, where p(n) denotes n-th prime.
A116459: Numbers n such that the minimal length of the corresponding shortest addition chain A003313(n)=A003313(3*n).
A140966: (5+(-2)^n)/3.
A159288: Expansion of (1+x+x^2)/(1-x^2-2*x^3).
A167053: a(1)=3, else a(n)=1+a(n-1)+gcd( a(n-1)*(a(n-1)+2), A073829(a(n-1)) ).
A246065: a(n) = sum_{k=0..n}C(n,k)^2*C(2k,k)/(2k-1), where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
A247608: a(n) = Sum_{k=0..3} binomial(6,k)*binomial(n,k).

Number of the day: 6939

Properties of the number 6939:

6939 = 3³ × 257 is the 6048^th composite number and is not squarefree.
6939 has 2 distinct prime factors, 8 divisors, 7 antidivisors and 4608 totatives.
6939 = 3470² - 3469² = 1158² - 1155² = 390² - 381² = 142² - 115² is the difference of 2 nonnegative squares in 4 ways.
6939 is the sum of 2 positive triangular numbers.
6939 is the difference of 2 positive pentagonal numbers in 1 way.
6939 = 13² + 23² + 79² is the sum of 3 positive squares.
6939² = 864² + 6885² is the sum of 2 positive squares in 1 way.
6939² is the sum of 3 positive squares.
6939 is a divisor of 1783⁴ - 1.
6939 = '6' + '939' is the concatenation of 2 semiprime numbers.
6939 is palindromic in (at least) the following bases: 2, 29, and -51.
6939 in base 16 = 1b1b and consists of only the digits '1' and 'b'.
6939 in base 21 = ff9 and consists of only the digits '9' and 'f'.
6939 in base 28 = 8nn and consists of only the digits '8' and 'n'.
6939 in base 29 = 878 and consists of only the digits '7' and '8'.

The number 6939 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033681: a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A048710: Family 1 "Rule 90 x Rule 150 Array" read by antidiagonals.
A068221: An auxiliary bit-mask sequence for computing A066425. (The "clean", symmetric one).
A074338: a(1) = 2; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A107264: Expansion of (1-3x-sqrt((1-3x)^2-4*3*x^2))/(2*3*x^2).
A107267: A square array of Motzkin related transforms, read by antidiagonals.
A111471: a(1) = 1; for n>1, a(n) = least k such that concatenation of n copies of k with all previous concatenations gives a prime.
A195278: T(n,k)=Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by k or less and triangles differing by a constant counted only once
A223556: T(n,k)=Petersen graph (3,1) coloring a rectangular array: number of nXk 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0
A249184: A249183 seen as binary numbers.

Number of the day: 71229576238051

Properties of the number 71229576238051:

71229576238051 = 7 × 11 × 67 × 8693 × 1588273 is composite and squarefree.
71229576238051 has 5 distinct prime factors, 32 divisors, 59 antidivisors and 54668830487040 totatives.
71229576238051 has an emirpimes digit sum 58 in base 10.
71229576238051 is the difference of 2 nonnegative squares in 16 ways.
71229576238051 is the sum of 2 positive triangular numbers.
71229576238051 is the difference of 2 positive pentagonal numbers in 15 ways.
71229576238051 = 5519² + 14709² + 8439747² is the sum of 3 positive squares.
71229576238051² = 12816204864925² + 70067092303824² = 3353757457820² + 71150578648149² = 28322726236420² + 65356527673899² = 16101014299755² + 69385948646476² is the sum of 2 positive squares in 4 ways.
71229576238051² is the sum of 3 positive squares.
71229576238051 is a divisor of 967^12025488 - 1.
71229576238051 = '71' + '229576238051' is the concatenation of 2 prime numbers.
71229576238051 = '71229' + '576238051' is the concatenation of 2 semiprime numbers.
71229576238051 = '712295' + '76238051' is the concatenation of 2 sphenic numbers.

Number of the day: 72637

Properties of the number 72637:

72637 = 19 × 3823 is semiprime and squarefree.
72637 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 68796 totatives.
72637 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 72637 results in a sphenic number.
72637 = 36319² - 36318² = 1921² - 1902² is the difference of 2 nonnegative squares in 2 ways.
72637 is the difference of 2 positive pentagonal numbers in 2 ways.
72637 = 12² + 77² + 258² is the sum of 3 positive squares.
72637² is the sum of 3 positive squares.
72637 is a divisor of 353²¹ - 1.
72637 is an emirpimes in (at least) the following bases: 2, 3, 5, 9, 12, 13, 14, 16, 27, 28, 36, 38, 39, 40, 47, 50, 56, 57, 71, 77, 78, 80, 81, 86, 88, 89, 91, 96, and 98.
72637 is palindromic in (at least) the following bases: 44, and 58.
72637 in base 44 = bMb and consists of only the digits 'M' and 'b'.
72637 in base 58 = LYL and consists of only the digits 'L' and 'Y'.

Number of the day: 50299301

Georg Cantor was born on this day 172 years ago.

Properties of the number 50299301:

50299301 = 13² × 297629 is the 47281334^th composite number and is not squarefree.
50299301 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 46429968 totatives.
50299301 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 50299301 results in a sphenic number.
50299301 = 25149651² - 25149650² = 1934595² - 1934582² = 148899² - 148730² is the difference of 2 nonnegative squares in 3 ways.
50299301 is the difference of 2 positive pentagonal numbers in 3 ways.
50299301 = 4255² + 5674² = 974² + 7025² = 3601² + 6110² is the sum of 2 positive squares in 3 ways.
50299301 = 34² + 41² + 7092² is the sum of 3 positive squares.
50299301² = 19345885² + 46430124² = 5565976² + 49990395² = 31248165² + 39415376² = 24364899² + 44004220² = 35417851² + 35715480² = 13684700² + 48401949² = 14089251² + 48285740² is the sum of 2 positive squares in 7 ways.
50299301² is the sum of 3 positive squares.
50299301 is a divisor of 1451⁸⁰⁴⁴ - 1.
50299301 = '502' + '99301' is the concatenation of 2 semiprime numbers.

Number of the day: 55334

Properties of the number 55334:

55334 = 2 × 73 × 379 is a sphenic number and squarefree.
55334 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 27216 totatives.
55334 has an oblong digit sum 20 in base 10.
55334 is the sum of 2 positive triangular numbers.
55334 = 3² + 10² + 235² is the sum of 3 positive squares.
55334² = 36384² + 41690² is the sum of 2 positive squares in 1 way.
55334² is the sum of 3 positive squares.
55334 is a divisor of 757⁴ - 1.
55334 = '55' + '334' is the concatenation of 2 semiprime numbers.
55334 is palindromic in (at least) base 91.

The number 55334 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A037238: x->5x-1 if x odd, else x->x/2.

Number of the day: 1283

Properties of the number 1283:

1283 is the 208^th prime.
1283 has 17 antidivisors and 1282 totatives.
1283 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 1283 results in an emirp.
1283 = 642² - 641² is the difference of 2 nonnegative squares in 1 way.
1283 is the difference of 2 positive pentagonal numbers in 1 way.
1283 = 3² + 7² + 35² is the sum of 3 positive squares.
1283² is the sum of 3 positive squares.
1283 is a divisor of 3⁶⁴¹ - 1.
1283 is an emirp in (at least) the following bases: 5, 6, 7, 10, 13, 16, 19, 29, 30, 32, 35, 36, 41, 44, 45, 46, 49, 51, 53, 54, 55, 59, 66, 71, 73, 74, 75, 77, 83, 87, 89, 92, and 96.
1283 is palindromic in (at least) the following bases: 20, and 21.
1283 in base 6 = 5535 and consists of only the digits '3' and '5'.
1283 in base 13 = 779 and consists of only the digits '7' and '9'.
1283 in base 19 = 3aa and consists of only the digits '3' and 'a'.
1283 in base 20 = 343 and consists of only the digits '3' and '4'.
1283 in base 21 = 2j2 and consists of only the digits '2' and 'j'.
1283 in base 35 = 11n and consists of only the digits '1' and 'n'.

The number 1283 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000057: Primes dividing all Fibonacci sequences.
A005265: a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=smallest prime factor of b(n)-1.
A005385: Safe primes p: (p-1)/2 is also prime.
A023202: Numbers n such that n and n + 8 both prime.
A034253: Triangle read by rows: T(n,k) = number of inequivalent linear [n,k] binary codes without 0 columns (n >= 1, 1 <= k <= n).
A046132: Larger member p+4 of cousin primes (p, p+4).
A048988: Primes of form 4n^2 + 4n + 59.
A065720: Primes whose binary representation is also the decimal representation of a prime.
A175791: Primes that become another prime under the map 1 <-> 0 (acting on the digits: A222210), cf. A171013.
A213891: Fixed points of the sequence A262212 defined by the minimum number of 2's in the relation n*[n,2,2,...,2,n] = [x,...,x] between simple continued fractions.