Number of the day: 245158254

Properties of the number 245158254:

245158254 = 2 × 3² × 11 × 19 × 65167 is the 231729379^th composite number and is not squarefree.
245158254 has 5 distinct prime factors, 48 divisors, 29 antidivisors and 70379280 totatives.
245158254 has a triangular digit sum 36 in base 10.
245158254 = 238³ + 285³ + 593³ is the sum of 3 positive cubes in 1 way.
245158254 is the difference of 2 positive pentagonal numbers in 4 ways.
245158254 = 50² + 277² + 15655² is the sum of 3 positive squares.
245158254² is the sum of 3 positive squares.
245158254 is a proper divisor of 683²¹⁷²² - 1.
245158254 = '24515' + '8254' is the concatenation of 2 semiprime numbers.

Number of the day: 5328

Properties of the number 5328:

5328 = 2⁴ × 3² × 37 is the 4622^th composite number and is not squarefree.
5328 has 3 distinct prime factors, 30 divisors, 7 antidivisors and 1728 totatives.
5328 has an oblong digit product 240 in base 10.
5328 is the difference of 2 nonnegative squares in 9 ways.
5328 is the sum of 2 positive triangular numbers.
5328 is the difference of 2 positive pentagonal numbers in 1 way.
5328 = 12² + 72² is the sum of 2 positive squares in 1 way.
5328 = 16² + 44² + 56² is the sum of 3 positive squares.
5328² = 1728² + 5040² is the sum of 2 positive squares in 1 way.
5328² is the sum of 3 positive squares.
5328 is a proper divisor of 73² - 1.
5328 is palindromic in (at least) the following bases: 11, and 73.
5328 in base 6 = 40400 and consists of only the digits '0' and '4'.
5328 in base 11 = 4004 and consists of only the digits '0' and '4'.
5328 in base 17 = 1177 and consists of only the digits '1' and '7'.
5328 in base 19 = ee8 and consists of only the digits '8' and 'e'.
5328 in base 36 = 440 and consists of only the digits '0' and '4'.
5328 in base 51 = 22O and consists of only the digits '2' and 'O'.

The number 5328 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033996: 8 times triangular numbers: a(n) = 4*n*(n+1).
A084920: a(n) = (prime(n)-1)*(prime(n)+1).
A106302: Period of the Fibonacci 3-step sequence A000073 mod prime(n).
A173116: a(n) = sinh(2*arcsinh(n))^2 = 4*n^2*(n^2 + 1).
A179669: Products of form p^4*q^2*r where p, q and r are three distinct primes.
A236278: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the upper median unequal to the lower median in every 2X2 subblock
A247726: T(n,k)=Number of length n+3 0..k arrays with no disjoint pairs in any consecutive four terms having the same sum
A248925: Triangle in which row n consists of the coefficients in Sum_{m=0..n} x^m * Product_{k=m+1..n} (1-k*x), as read by rows.
A257368: Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit.
A317707: Number of powerful rooted trees with n nodes.

Number of the day: 286345

John Forbes Nash, Jr. was born on this day 91 years ago.

Properties of the number 286345:

286345 is a cyclic number.
286345 = 5 × 57269 is semiprime and squarefree.
286345 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 229072 totatives.
286345 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 286345 results in an emirpimes.
286345 = 143173² - 143172² = 28637² - 28632² is the difference of 2 nonnegative squares in 2 ways.
286345 is the sum of 2 positive triangular numbers.
286345 is the difference of 2 positive pentagonal numbers in 2 ways.
286345 = 288² + 451² = 188² + 501² is the sum of 2 positive squares in 2 ways.
286345 = 44² + 75² + 528² is the sum of 3 positive squares.
286345² = 188376² + 215657² = 171807² + 229076² = 120457² + 259776² = 59500² + 280095² is the sum of 2 positive squares in 4 ways.
286345² is the sum of 3 positive squares.
286345 is a proper divisor of 1429²⁷⁸ - 1.
286345 = '286' + '345' is the concatenation of 2 sphenic numbers.
286345 is an emirpimes in (at least) the following bases: 2, 10, 22, 25, 28, 29, 37, 38, 41, 43, 48, 52, 55, 57, 60, 63, 65, 67, 71, 72, 73, 77, 82, 91, 92, 93, and 99.

Number of the day: 712398

Vladimir Igorevich Arnold was born on this day 82 years ago.

Properties of the number 712398:

712398 = 2 × 3 × 37 × 3209 is the 654913^th composite number and is squarefree.
712398 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 230976 totatives.
712398 has a sphenic digit sum 30 in base 10.
712398 has an oblong digit sum 30 in base 10.
712398 is the sum of 2 positive triangular numbers.
712398 is the difference of 2 positive pentagonal numbers in 4 ways.
712398 = 17² + 122² + 835² is the sum of 3 positive squares.
712398² = 470640² + 534798² = 353250² + 618648² = 271752² + 658530² = 231048² + 673890² is the sum of 2 positive squares in 4 ways.
712398² is the sum of 3 positive squares.
712398 is a proper divisor of 1021⁷² - 1.
712398 is palindromic in (at least) base -96.

Number of the day: 771577455

Properties of the number 771577455:

771577455 = 3 × 5 × 11 × 4676227 is the 731819308^th composite number and is squarefree.
771577455 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 374098080 totatives.
Reversing the decimal digits of 771577455 results in a sphenic number.
771577455 = 385788728² - 385788727² = 128596244² - 128596241² = 77157748² - 77157743² = 35071708² - 35071697² = 25719256² - 25719241² = 11690584² - 11690551² = 7014368² - 7014313² = 2338196² - 2338031² is the difference of 2 nonnegative squares in 8 ways.
771577455 is the difference of 2 positive pentagonal numbers in 4 ways.
771577455 is not the sum of 3 positive squares.
771577455² = 462946473² + 617261964² is the sum of 2 positive squares in 1 way.
771577455² is the sum of 3 positive squares.
771577455 is a proper divisor of 199¹⁵⁰⁸⁴⁶ - 1.

Number of the day: 264666435

Properties of the number 264666435:

264666435 = 3 × 5 × 11 × 223 × 7193 is the 250229848^th composite number and is squarefree.
264666435 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 127729920 totatives.
264666435 has a sphenic digit sum 42 in base 10.
264666435 has an oblong digit sum 42 in base 10.
264666435 is the difference of 2 nonnegative squares in 16 ways.
264666435 is the difference of 2 positive pentagonal numbers in 7 ways.
264666435 = 427² + 845² + 16241² is the sum of 3 positive squares.
264666435² = 101289276² + 244517493² = 65679075² + 256387560² = 165702603² + 206375796² = 158799861² + 211733148² is the sum of 2 positive squares in 4 ways.
264666435² is the sum of 3 positive squares.
264666435 is a proper divisor of 967⁴⁴⁴ - 1.
264666435 = '264666' + '435' is the concatenation of 2 sphenic numbers.

Number of the day: 791708

John Edensor Littlewood was born on this day 134 years ago.

Properties of the number 791708:

791708 = 2² × 197927 is the 728373^th composite number and is not squarefree.
791708 has 2 distinct prime factors, 6 divisors, 33 antidivisors and 395852 totatives.
Reversing the decimal digits of 791708 results in a prime.
791708 = 197928² - 197926² is the difference of 2 nonnegative squares in 1 way.
791708 is the difference of 2 positive pentagonal numbers in 1 way.
791708 is not the sum of 3 positive squares.
791708² is the sum of 3 positive squares.
791708 is a proper divisor of 17⁹⁸⁹⁶³ - 1.
791708 is palindromic in (at least) base -93.

Number of the day: 80997

Properties of the number 80997:

80997 = 3 × 7² × 19 × 29 is the 73071^th composite number and is not squarefree.
80997 has 4 distinct prime factors, 24 divisors, 35 antidivisors and 42336 totatives.
80997 has a semiprime digit sum 33 in base 10.
80997 is the difference of 2 nonnegative squares in 12 ways.
80997 is the sum of 2 positive triangular numbers.
80997 is the difference of 2 positive pentagonal numbers in 4 ways.
80997 = 17² + 82² + 272² is the sum of 3 positive squares.
80997² = 55860² + 58653² is the sum of 2 positive squares in 1 way.
80997² is the sum of 3 positive squares.
80997 is a proper divisor of 521⁶ - 1.
80997 = '809' + '97' is the concatenation of 2 prime numbers.
80997 in base 34 = 2229 and consists of only the digits '2' and '9'.

Number of the day: 763132

Properties of the number 763132:

763132 = 2² × 190783 is the 701917^th composite number and is not squarefree.
763132 has 2 distinct prime factors, 6 divisors, 23 antidivisors and 381564 totatives.
763132 has a semiprime digit sum 22 in base 10.
763132 has an oblong digit product 756 in base 10.
Reversing the decimal digits of 763132 results in a prime.
763132 = 190784² - 190782² is the difference of 2 nonnegative squares in 1 way.
763132 is the sum of 2 positive triangular numbers.
763132 is the difference of 2 positive pentagonal numbers in 1 way.
763132 is not the sum of 3 positive squares.
763132² is the sum of 3 positive squares.
763132 is a proper divisor of 601³⁵³³ - 1.

Number of the day: 2307484

Aleksandr Mikhailovich Lyapunov was born on this day 162 years ago.

Properties of the number 2307484:

2307484 = 2² × 733 × 787 is the 2137465^th composite number and is not squarefree.
2307484 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 1150704 totatives.
2307484 has a triangular digit sum 28 in base 10.
2307484 = 576872² - 576870² = 1520² - 54² is the difference of 2 nonnegative squares in 2 ways.
2307484 is the difference of 2 positive pentagonal numbers in 3 ways.
2307484 is not the sum of 3 positive squares.
2307484² = 339984² + 2282300² is the sum of 2 positive squares in 1 way.
2307484² is the sum of 3 positive squares.
2307484 is a proper divisor of 379⁷³² - 1.

Number of the day: 909307

Properties of the number 909307:

909307 is a cyclic number.
909307 = 7 × 129901 is semiprime and squarefree.
909307 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 779400 totatives.
909307 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 909307 results in an emirpimes.
909307 = 19³ + 53³ + 91³ is the sum of 3 positive cubes in 1 way.
909307 = 454654² - 454653² = 64954² - 64947² is the difference of 2 nonnegative squares in 2 ways.
909307 is the difference of 2 positive pentagonal numbers in 2 ways.
909307 = 153² + 163² + 927² is the sum of 3 positive squares.
909307² = 439740² + 795907² is the sum of 2 positive squares in 1 way.
909307² is the sum of 3 positive squares.
909307 is a proper divisor of 113⁴³³ - 1.
909307 is an emirpimes in (at least) the following bases: 2, 10, 14, 16, 17, 21, 23, 25, 28, 30, 34, 37, 38, 40, 51, 53, 54, 56, 59, 61, 73, 78, 79, 81, 84, 85, 86, 87, 93, and 95.

Number of the day: 462130872

Properties of the number 462130872:

462130872 = 2³ × 3 × 7 × 2750779 is the 437669513^th composite number and is not squarefree.
462130872 has 4 distinct prime factors, 32 divisors, 69 antidivisors and 132037344 totatives.
462130872 has a semiprime digit sum 33 in base 10.
462130872 = 115532719² - 115532717² = 57766361² - 57766357² = 38510909² - 38510903² = 19255459² - 19255447² = 16504681² - 16504667² = 8252351² - 8252323² = 5501579² - 5501537² = 2750821² - 2750737² is the difference of 2 nonnegative squares in 8 ways.
462130872 = 242² + 772² + 21482² is the sum of 3 positive squares.
462130872² is the sum of 3 positive squares.
462130872 is a proper divisor of 71³⁰⁵⁶⁴² - 1.
462130872 = '46213087' + '2' is the concatenation of 2 prime numbers.

Number of the day: 9331

Properties of the number 9331:

9331 = 7 × 31 × 43 is a sphenic number and squarefree.
9331 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 7560 totatives.
Reversing the decimal digits of 9331 results in a semiprime.
9331 = 19² + … + 32² is the sum of at least 2 consecutive positive squares in 1 way.
9331 = 20³ + 11³ is the sum of 2 positive cubes in 1 way.
9331 = 4666² - 4665² = 670² - 663² = 166² - 135² = 130² - 87² is the difference of 2 nonnegative squares in 4 ways.
9331 is the sum of 2 positive triangular numbers.
9331 is the difference of 2 positive pentagonal numbers in 4 ways.
9331 = 9² + 41² + 87² is the sum of 3 positive squares.
9331² is the sum of 3 positive squares.
9331 is a proper divisor of 37⁶ - 1.
9331 is palindromic in (at least) the following bases: 6, 36, 53, -6, and -37.
9331 in base 6 = 111111 and consists of only the digit '1'.
9331 in base 35 = 7ll and consists of only the digits '7' and 'l'.
9331 in base 36 = 777 and consists of only the digit '7'.
9331 in base 52 = 3NN and consists of only the digits '3' and 'N'.
9331 in base 53 = 3H3 and consists of only the digits '3' and 'H'.

The number 9331 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003464: a(n) = (6^n - 1)/5.
A005937: Pseudoprimes to base 6.
A022170: Triangle of Gaussian binomial coefficients [ n,k ] for q = 6.
A023037: a(n) = n^0+n^1+...+n^(n-1), or a(n) = (n^n-1)/(n-1) with a(0)=0; a(1)=1.
A025012: Central heptanomial coefficients: largest coefficient of (1+x+...+x^6)^n.
A053700: a(n) = 111111 in base n.
A057075: Table read by antidiagonals of T(n,k)=floor[n^n/k] with n,k >= 1.
A125118: Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n.
A201552: Square array read by diagonals: T(n,k) = number of arrays of n integers in -k..k with sum equal to 0.
A262508: Numbers that occur only once in A155043; positions of zeros in A262505, ones in A262507.

Number of the day: 3816

Properties of the number 3816:

3816 = 2³ × 3² × 53 is the 3286^th composite number and is not squarefree.
3816 has 3 distinct prime factors, 24 divisors, 9 antidivisors and 1248 totatives.
3816 has a Fibonacci digit product 144 in base 10.
3816 = 7³ + 9³ + 14³ is the sum of 3 positive cubes in 1 way.
3816 = 955² - 953² = 479² - 475² = 321² - 315² = 165² - 153² = 115² - 97² = 71² - 35² is the difference of 2 nonnegative squares in 6 ways.
3816 is the difference of 2 positive pentagonal numbers in 1 way.
3816 = 30² + 54² is the sum of 2 positive squares in 1 way.
3816 = 14² + 16² + 58² is the sum of 3 positive squares.
3816² = 2016² + 3240² is the sum of 2 positive squares in 1 way.
3816² is the sum of 3 positive squares.
3816 is a proper divisor of 107² - 1.
3816 = '381' + '6' is the concatenation of 2 semiprime numbers.
3816 is palindromic in (at least) the following bases: 31, 71, and -41.
3816 in base 16 = ee8 and consists of only the digits '8' and 'e'.
3816 in base 19 = aag and consists of only the digits 'a' and 'g'.
3816 in base 31 = 3u3 and consists of only the digits '3' and 'u'.
3816 in base 43 = 22W and consists of only the digits '2' and 'W'.
3816 in base 61 = 11Y and consists of only the digits '1' and 'Y'.

The number 3816 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000567: Octagonal numbers: n*(3*n-2). Also called star numbers.
A014642: Even octagonal numbers: 4*n*(3*n-1).
A118807: Number of partitions of n having no parts with multiplicity 3.
A135190: Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=5.
A138990: a(n) = Frobenius number for 4 successive primes = F[p(n),p(n+1),p(n+2),p(n+3)].
A139229: First differences of perfect numbers A000396, divided by 2.
A173682: Number of ways of writing n as a sum of 9 nonnegative cubes.
A219047: Numbers n such that 3^n - 28 is prime.
A257211: Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit.
A269656: T(n,k)=Number of length-n 0..k arrays with no adjacent pair x,x+1 repeated.

Number of the day: 950

Properties of the number 950:

950 = 2 × 5² × 19 is the 788^th composite number and is not squarefree.
950 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 360 totatives.
950 has a semiprime digit sum 14 in base 10.
950 is the difference of 2 positive pentagonal numbers in 2 ways.
950 = 3² + 10² + 29² is the sum of 3 positive squares.
950² = 570² + 760² = 266² + 912² is the sum of 2 positive squares in 2 ways.
950² is the sum of 3 positive squares.
950 is a proper divisor of 151² - 1.
950 is palindromic in (at least) the following bases: 37, 49, 94, -15, and -73.
950 in base 6 = 4222 and consists of only the digits '2' and '4'.
950 in base 7 = 2525 and consists of only the digits '2' and '5'.
950 in base 8 = 1666 and consists of only the digits '1' and '6'.
950 in base 30 = 11k and consists of only the digits '1' and 'k'.

The number 950 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000601: Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A005449: Second pentagonal numbers: a(n) = n*(3*n + 1)/2.
A023894: Number of partitions of n into prime power parts (1 excluded).
A024702: a(n) = (prime(n)^2 - 1)/24.
A028338: Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x.
A028895: 5 times triangular numbers: a(n) = 5*n*(n+1)/2.
A035959: Number of partitions of n in which no parts are multiples of 5.
A084646: Hypotenuses for which there exist exactly 2 distinct integer triangles.
A304714: Number of connected strict integer partitions of n.

Number of the day: 586134

Properties of the number 586134:

586134 = 2 × 3² × 32563 is the 538078^th composite number and is not squarefree.
586134 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 195372 totatives.
586134 is the sum of 2 positive triangular numbers.
586134 = 17² + 82² + 761² is the sum of 3 positive squares.
586134² is the sum of 3 positive squares.
586134 is a proper divisor of 541²⁰¹ - 1.
586134 = '58' + '6134' is the concatenation of 2 semiprime numbers.

Number of the day: 71311

Properties of the number 71311:

71311 is a cyclic number.
71311 = 29 × 2459 is semiprime and squarefree.
71311 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 68824 totatives.
71311 has an emirp digit sum 13 in base 10.
71311 has a Fibonacci digit sum 13 in base 10.
71311 has a semiprime digit product 21 in base 10.
71311 has a Fibonacci digit product 21 in base 10.
71311 has a triangular digit product 21 in base 10.
Reversing the decimal digits of 71311 results in a prime.
71311 = 35656² - 35655² = 1244² - 1215² is the difference of 2 nonnegative squares in 2 ways.
71311 is the sum of 2 positive triangular numbers.
71311 is the difference of 2 positive pentagonal numbers in 2 ways.
71311 is not the sum of 3 positive squares.
71311² = 49180² + 51639² is the sum of 2 positive squares in 1 way.
71311² is the sum of 3 positive squares.
71311 is a proper divisor of 59¹²²⁹ - 1.
71311 = '71' + '311' is the concatenation of 2 emirps.
71311 is an emirpimes in (at least) the following bases: 5, 7, 9, 14, 15, 21, 23, 25, 26, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 47, 55, 56, 61, 63, 65, 68, 69, 71, 79, 83, 85, 89, 93, 95, 96, 97, and 100.
71311 is palindromic in (at least) the following bases: -48, -53, and -56.
71311 in base 44 = aaV and consists of only the digits 'V' and 'a'.
71311 in base 52 = QJJ and consists of only the digits 'J' and 'Q'.
71311 in base 54 = OOV and consists of only the digits 'O' and 'V'.
71311 in base 55 = NVV and consists of only the digits 'N' and 'V'.

Number of the day: 65919

Properties of the number 65919:

65919 = 3 × 7 × 43 × 73 is the 59336^th composite number and is squarefree.
65919 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 36288 totatives.
65919 has a sphenic digit sum 30 in base 10.
65919 has an oblong digit sum 30 in base 10.
65919 = 62² + … + 75² is the sum of at least 2 consecutive positive squares in 1 way.
65919 = 32960² - 32959² = 10988² - 10985² = 4712² - 4705² = 1580² - 1559² = 788² - 745² = 488² - 415² = 320² - 191² = 260² - 41² is the difference of 2 nonnegative squares in 8 ways.
65919 is the sum of 2 positive triangular numbers.
65919 is the difference of 2 positive pentagonal numbers in 3 ways.
65919 is not the sum of 3 positive squares.
65919² = 43344² + 49665² is the sum of 2 positive squares in 1 way.
65919² is the sum of 3 positive squares.
65919 is a proper divisor of 1597³ - 1.
65919 = '659' + '19' is the concatenation of 2 prime numbers.
65919 = '6' + '5919' is the concatenation of 2 semiprime numbers.
65919 in base 60 = IId and consists of only the digits 'I' and 'd'.

The number 65919 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A129212: Numbers n such that n^3 divides 4^(n^2)-1.
A186570: T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
A249614: Integers that reach the (47360, 29127) cycle described in A234534, after iterations of numerator(sigma(n)/n) = A017665(n).

Number of the day: 829600

Properties of the number 829600:

829600 = 2⁵ × 5² × 17 × 61 is the 763470^th composite number and is not squarefree.
829600 has 4 distinct prime factors, 72 divisors, 15 antidivisors and 307200 totatives.
829600 has a semiprime digit sum 25 in base 10.
829600 is the difference of 2 nonnegative squares in 24 ways.
829600 is the difference of 2 positive pentagonal numbers in 5 ways.
829600 = 300² + 860² = 140² + 900² = 636² + 652² = 508² + 756² = 428² + 804² = 276² + 868² is the sum of 2 positive squares in 6 ways.
829600 = 68² + 240² + 876² is the sum of 3 positive squares.
829600² = 390400² + 732000² = 252000² + 790400² = 516000² + 649600² = 126880² + 819840² = 23040² + 829280² = 272640² + 783520² = 351360² + 751520² = 210080² + 802560² = 481120² + 675840² = 579744² + 593408² = 463232² + 688224² = 479136² + 677248² = 169824² + 812032² = 20608² + 829344² = 313472² + 768096² = 497760² + 663680² = 369920² + 742560² = 563040² + 609280² = 149600² + 816000² = 232288² + 796416² = 84864² + 825248² = 372096² + 741472² is the sum of 2 positive squares in 22 ways.
829600² is the sum of 3 positive squares.
829600 is a proper divisor of 599⁴ - 1.

The number 829600 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A209346: Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

Number of the day: 24682

Properties of the number 24682:

24682 = 2 × 7 × 41 × 43 is the 21949^th composite number and is squarefree.
24682 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 10080 totatives.
24682 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 24682 results in a semiprime.
24682 is the sum of 2 positive triangular numbers.
24682 is the difference of 2 positive pentagonal numbers in 5 ways.
24682 = 24² + 65² + 141² is the sum of 3 positive squares.
24682² = 5418² + 24080² is the sum of 2 positive squares in 1 way.
24682² is the sum of 3 positive squares.
24682 is a proper divisor of 1721² - 1.
24682 is palindromic in (at least) the following bases: 48, 62, and -9.
24682 in base 18 = 4434 and consists of only the digits '3' and '4'.
24682 in base 48 = AYA and consists of only the digits 'A' and 'Y'.
24682 in base 55 = 88g and consists of only the digits '8' and 'g'.
24682 in base 61 = 6cc and consists of only the digits '6' and 'c'.
24682 in base 62 = 6Q6 and consists of only the digits '6' and 'Q'.

The number 24682 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000970: Fermat coefficients.
A008646: Molien series for cyclic group of order 5.
A051170: T(n,5), array T as in A051168; a count of Lyndon words; aperiodic necklaces with 5 black beads and n-5 white beads.
A065345: a(n) = Mod( binomial(2*n,n), (n+1)*(n+2)*(n+3) ).
A157363: 686n - 14.
A234042: a(n) = C(n+4,4)*gcd(n,5)/5.
A234513: 8*binomial(9*n+8,n)/(9*n+8).
A241546: Number of partitions p of n such that (number of numbers of the form 3k in p) is a part of p.
A259110: 2*A000447(n).
A263226: a(n) = 15*n^2 - 13*n.

Number of the day: 28338496

Properties of the number 28338496:

28338496 = 2⁶ × 442789 is the 26577260^th composite number and is not squarefree.
28338496 has 2 distinct prime factors, 14 divisors, 37 antidivisors and 14169216 totatives.
28338496 has a prime digit sum 43 in base 10.
Reversing the decimal digits of 28338496 results in a semiprime.
28338496 = 7084625² - 7084623² = 3542314² - 3542310² = 1771160² - 1771152² = 885586² - 885570² = 442805² - 442773² is the difference of 2 nonnegative squares in 5 ways.
28338496 is the difference of 2 positive pentagonal numbers in 1 way.
28338496 = 1400² + 5136² is the sum of 2 positive squares in 1 way.
28338496 = 384² + 904² + 5232² is the sum of 3 positive squares.
28338496² = 14380800² + 24418496² is the sum of 2 positive squares in 1 way.
28338496² is the sum of 3 positive squares.
28338496 is a proper divisor of 641³⁶⁸⁹⁹ - 1.

Number of the day: 583006392

Edward Norton Lorenz was born on this day 102 years ago.

Properties of the number 583006392:

583006392 = 2³ × 3² × 23 × 352057 is the 552523140^th composite number and is not squarefree.
583006392 has 4 distinct prime factors, 48 divisors, 39 antidivisors and 185885568 totatives.
583006392 has a triangular digit sum 36 in base 10.
583006392 is the difference of 2 nonnegative squares in 12 ways.
583006392 is the difference of 2 positive pentagonal numbers in 2 ways.
583006392 = 22² + 412² + 24142² is the sum of 3 positive squares.
583006392² = 114769080² + 571598208² is the sum of 2 positive squares in 1 way.
583006392² is the sum of 3 positive squares.
583006392 is a proper divisor of 829⁵⁸⁶⁷⁶ - 1.

Number of the day: 43812311292

Properties of the number 43812311292:

43812311292 = 2² × 3⁴ × 47 × 1229 × 2341 is composite and not squarefree.
43812311292 has 5 distinct prime factors, 120 divisors, 47 antidivisors and 14275647360 totatives.
43812311292 has a triangular digit sum 36 in base 10.
43812311292 is the difference of 2 nonnegative squares in 20 ways.
43812311292 is the sum of 2 positive triangular numbers.
43812311292 is the difference of 2 positive pentagonal numbers in 2 ways.
43812311292 is not the sum of 3 positive squares.
43812311292² = 29690336160² + 32218047108² = 25826992560² + 35390465892² = 21627414720² + 38102146308² = 4990824720² + 43527121308² is the sum of 2 positive squares in 4 ways.
43812311292² is the sum of 3 positive squares.
43812311292 is a proper divisor of 1861²⁴⁸⁴ - 1.

Number of the day: 250514

Properties of the number 250514:

250514 = 2 × 11 × 59 × 193 is the 228435^th composite number and is squarefree.
250514 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 111360 totatives.
250514 has an emirp digit sum 17 in base 10.
250514 is the difference of 2 positive pentagonal numbers in 4 ways.
250514 = 28² + 93² + 491² is the sum of 3 positive squares.
250514² = 123310² + 218064² is the sum of 2 positive squares in 1 way.
250514² is the sum of 3 positive squares.
250514 is a proper divisor of 709⁶⁰ - 1.
250514 is palindromic in (at least) base 98.

Number of the day: 995262831

Properties of the number 995262831:

995262831 = 3² × 23 × 4808033 is the 944643956^th composite number and is not squarefree.
995262831 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 634660224 totatives.
995262831 has a triangular digit sum 45 in base 10.
995262831 = 497631416² - 497631415² = 165877140² - 165877137² = 55292384² - 55292375² = 21636160² - 21636137² = 7212084² - 7212015² = 2404120² - 2403913² is the difference of 2 nonnegative squares in 6 ways.
995262831 is the sum of 2 positive triangular numbers.
995262831 is the difference of 2 positive pentagonal numbers in 2 ways.
995262831 is not the sum of 3 positive squares.
995262831² = 298828305² + 949341744² is the sum of 2 positive squares in 1 way.
995262831² is the sum of 3 positive squares.
995262831 is a proper divisor of 47⁹⁰¹⁵⁰⁶ - 1.
995262831 = '995' + '262831' is the concatenation of 2 semiprime numbers.

Number of the day: 44681

Properties of the number 44681:

44681 = 7 × 13 × 491 is a sphenic number and squarefree.
44681 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 35280 totatives.
44681 has a prime digit sum 23 in base 10.
44681 = 22341² - 22340² = 3195² - 3188² = 1725² - 1712² = 291² - 200² is the difference of 2 nonnegative squares in 4 ways.
44681 is the difference of 2 positive pentagonal numbers in 3 ways.
44681 = 31² + 54² + 202² is the sum of 3 positive squares.
44681² = 17185² + 41244² is the sum of 2 positive squares in 1 way.
44681² is the sum of 3 positive squares.
44681 is a proper divisor of 983¹² - 1.
44681 = '4' + '4681' is the concatenation of 2 semiprime numbers.
44681 is palindromic in (at least) the following bases: -8, and -38.

The number 44681 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A016261: Expansion of 1/((1-x)*(1-9*x)*(1-10*x)).
A021404: Expansion of 1/((1-x)(1-3x)(1-4x)(1-12x)).
A156754: Numerator of Euler(n, 7/20).
A184322: Number of strings of numbers x(i=1..7) in 0..n with sum i^2*x(i)^3 equal to 49*n^3
A274037: Numbers k such that 3*10^k - 49 is prime.

Number of the day: 4842497080

Bertrand Russell was born on this day 147 years ago.

Properties of the number 4842497080:

4842497080 = 2³ × 5 × 121062427 is the 4614599637^th composite number and is not squarefree.
4842497080 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 1936998816 totatives.
4842497080 has a semiprime digit sum 46 in base 10.
4842497080 = 1210624271² - 1210624269² = 605312137² - 605312133² = 242124859² - 242124849² = 121062437² - 121062417² is the difference of 2 nonnegative squares in 4 ways.
4842497080 is the sum of 2 positive triangular numbers.
4842497080 is the difference of 2 positive pentagonal numbers in 2 ways.
4842497080 = 2100² + 2186² + 69522² is the sum of 3 positive squares.
4842497080² = 2905498248² + 3873997664² is the sum of 2 positive squares in 1 way.
4842497080² is the sum of 3 positive squares.
4842497080 is a proper divisor of 41^20177071 - 1.

Number of the day: 579716

Properties of the number 579716:

579716 = 2² × 37 × 3917 is the 532148^th composite number and is not squarefree.
579716 has 3 distinct prime factors, 12 divisors, 39 antidivisors and 281952 totatives.
579716 has a semiprime digit sum 35 in base 10.
579716 = 144930² - 144928² = 3954² - 3880² is the difference of 2 nonnegative squares in 2 ways.
579716 is the difference of 2 positive pentagonal numbers in 2 ways.
579716 = 290² + 704² = 46² + 760² is the sum of 2 positive squares in 2 ways.
579716 = 74² + 196² + 732² is the sum of 3 positive squares.
579716² = 408320² + 411516² = 188016² + 548380² = 69920² + 575484² = 252784² + 521700² is the sum of 2 positive squares in 4 ways.
579716² is the sum of 3 positive squares.
579716 is a proper divisor of 1087¹³² - 1.
579716 = '57971' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 869452037868

Pafnuty Lvovich Chebyshev was born on this day 198 years ago.

Properties of the number 869452037868:

869452037868 = 2² × 3 × 19 × 23 × 7523 × 22039 is composite and not squarefree.
869452037868 has 6 distinct prime factors, 96 divisors, 43 antidivisors and 262579420224 totatives.
869452037868 has a sphenic digit sum 66 in base 10.
869452037868 has a triangular digit sum 66 in base 10.
869452037868 is the difference of 2 nonnegative squares in 16 ways.
869452037868 is the sum of 2 positive triangular numbers.
869452037868 is the difference of 2 positive pentagonal numbers in 7 ways.
869452037868 = 1682² + 2930² + 932438² is the sum of 3 positive squares.
869452037868² is the sum of 3 positive squares.
869452037868 is a proper divisor of 1319²⁴⁸²²⁶ - 1.

Number of the day: 4488072

Properties of the number 4488072:

4488072 = 2³ × 3 × 187003 is the 4172892^th composite number and is not squarefree.
4488072 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 1496016 totatives.
4488072 has a semiprime digit sum 33 in base 10.
4488072 = 1122019² - 1122017² = 561011² - 561007² = 374009² - 374003² = 187009² - 186997² is the difference of 2 nonnegative squares in 4 ways.
4488072 is the sum of 2 positive triangular numbers.
4488072 = 32² + 262² + 2102² is the sum of 3 positive squares.
4488072² is the sum of 3 positive squares.
4488072 is a proper divisor of 241⁶⁹²⁶ - 1.
4488072 = '448807' + '2' is the concatenation of 2 prime numbers.

Number of the day: 3102432396

Properties of the number 3102432396:

3102432396 = 2² × 3 × 7 × 2069 × 17851 is the 2953292890^th composite number and is not squarefree.
3102432396 has 5 distinct prime factors, 48 divisors, 27 antidivisors and 885931200 totatives.
3102432396 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 3102432396 results in a sphenic number.
3102432396 = 775608100² - 775608098² = 258536036² - 258536030² = 110801164² - 110801150² = 36933740² - 36933698² = 376940² - 372802² = 131164² - 118750² = 68036² - 39070² = 61300² - 25598² is the difference of 2 nonnegative squares in 8 ways.
3102432396 is the difference of 2 positive pentagonal numbers in 4 ways.
3102432396 = 646² + 2446² + 55642² is the sum of 3 positive squares.
3102432396² = 1228077396² + 2849019600² is the sum of 2 positive squares in 1 way.
3102432396² is the sum of 3 positive squares.
3102432396 is a proper divisor of 647²⁸⁰⁵⁰ - 1.

Number of the day: 8794

Properties of the number 8794:

8794 = 2 × 4397 is semiprime and squarefree.
8794 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 4396 totatives.
8794 has a triangular digit sum 28 in base 10.
8794 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 8794 results in a sphenic number.
8794 is the sum of 2 positive triangular numbers.
8794 is the difference of 2 positive pentagonal numbers in 2 ways.
8794 = 35² + 87² is the sum of 2 positive squares in 1 way.
8794 = 12² + 55² + 75² is the sum of 3 positive squares.
8794² = 6090² + 6344² is the sum of 2 positive squares in 1 way.
8794² is the sum of 3 positive squares.
8794 is a proper divisor of 7¹⁵⁷ - 1.
8794 = '87' + '94' is the concatenation of 2 semiprime numbers.
8794 is an emirpimes in (at least) the following bases: 2, 3, 4, 14, 18, 19, 24, 26, 29, 30, 37, 45, 46, 60, 68, 69, 76, 77, 83, 85, 89, 93, 94, 98, and 100.
8794 is palindromic in (at least) the following bases: 56, and -59.
8794 in base 21 = jjg and consists of only the digits 'g' and 'j'.
8794 in base 55 = 2nn and consists of only the digits '2' and 'n'.
8794 in base 56 = 2j2 and consists of only the digits '2' and 'j'.

The number 8794 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A096403: Number of partitions of n in which number of least parts is equal to least part.
A126283: Largest number k for which the n-th prime is the median of the largest prime dividing the first k integers.
A129311: Numbers n such that 6*p(n)*p(n+1)*p(n+2)*p(n+3)*p(n+4)*p(n+5)-1 and 6*p(n)*p(n+1)*p(n+2)*p(n+3)*p(n+4)*p(n+5)+1 are twin primes with p(n)=n-th prime.
A206423: Fibonacci sequence beginning 12, 7.
A237871: Number of partitions of n such that (greatest part) + (least part) > number of parts.
A243718: Number of inequivalent (mod D_8) ways to place 3 nonattacking knights on an n X n board.
A270683: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 190", based on the 5-celled von Neumann neighborhood.
A301381: Number of tied close American football games: number of ways for the game to end at the score of n to n and never be separated by more than one score after each play.
A301604: Number of nX4 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
A301608: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Number of the day: 54199161

Properties of the number 54199161:

54199161 = 3² × 6022129 is the 50961795^th composite number and is not squarefree.
54199161 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 36132768 totatives.
54199161 has a triangular digit sum 36 in base 10.
54199161 = 27099581² - 27099580² = 9033195² - 9033192² = 3011069² - 3011060² is the difference of 2 nonnegative squares in 3 ways.
54199161 is the sum of 2 positive triangular numbers.
54199161 is the difference of 2 positive pentagonal numbers in 1 way.
54199161 = 2925² + 6756² is the sum of 2 positive squares in 1 way.
54199161 = 89² + 226² + 7358² is the sum of 3 positive squares.
54199161² = 37087911² + 39522600² is the sum of 2 positive squares in 1 way.
54199161² is the sum of 3 positive squares.
54199161 is a proper divisor of 521⁷¹⁶⁹² - 1.
54199161 = '5419' + '9161' is the concatenation of 2 prime numbers.
54199161 = '54199' + '161' is the concatenation of 2 semiprime numbers.

Number of the day: 2553

Properties of the number 2553:

2553 = 3 × 23 × 37 is a sphenic number and squarefree.
2553 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 1584 totatives.
2553 has an emirpimes digit sum 15 in base 10.
2553 has a triangular digit sum 15 in base 10.
2553 = 1277² - 1276² = 427² - 424² = 67² - 44² = 53² - 16² is the difference of 2 nonnegative squares in 4 ways.
2553 is the difference of 2 positive pentagonal numbers in 1 way.
2553 = 2² + 7² + 50² is the sum of 3 positive squares.
2553² = 828² + 2415² is the sum of 2 positive squares in 1 way.
2553² is the sum of 3 positive squares.
2553 is a proper divisor of 919⁴ - 1.
2553 is palindromic in (at least) the following bases: 2, 16, 19, 44, 68, -30, -34, -58, and -88.
2553 in base 11 = 1a11 and consists of only the digits '1' and 'a'.
2553 in base 16 = 9f9 and consists of only the digits '9' and 'f'.
2553 in base 18 = 7ff and consists of only the digits '7' and 'f'.
2553 in base 19 = 717 and consists of only the digits '1' and '7'.
2553 in base 29 = 311 and consists of only the digits '1' and '3'.
2553 in base 35 = 22x and consists of only the digits '2' and 'x'.
2553 in base 43 = 1GG and consists of only the digits '1' and 'G'.
2553 in base 44 = 1E1 and consists of only the digits '1' and 'E'.
2553 in base 50 = 113 and consists of only the digits '1' and '3'.

The number 2553 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001891: Hit polynomials; convolution of natural numbers with Fibonacci numbers F(2), F(3), F(4),....
A007853: Number of maximal antichains in rooted plane trees on n nodes.
A008778: a(n) = (n+1)*(n^2+8n+6)/6. Number of n-dimensional partitions of 4. Number of terms in 4th derivative of a function composed with itself n times.
A048701: List of binary palindromes of even length (written in base 10).
A051624: 12-gonal (or dodecagonal) numbers: a(n) = n*(5*n-4).
A056108: Fourth spoke of a hexagonal spiral.
A063489: a(n) = (2*n-1)*(5*n^2-5*n+6)/6.
A071355: a(n) = 2*n^2 + 11*n + 12.
A195162: Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, ...
A299285: Coordination sequence for "tea" 3D uniform tiling.

Number of the day: 823935734231

Properties of the number 823935734231:

823935734231 is a cyclic number.
823935734231 = 83 × 89 × 6553 × 17021 is composite and squarefree.
823935734231 has 4 distinct prime factors, 16 divisors, 39 antidivisors and 804692528640 totatives.
823935734231 = 411967867116² - 411967867115² = 4963468320² - 4963468237² = 4628852484² - 4628852395² = 62870340² - 62863787² = 55773000² - 55765613² = 24212016² - 24194995² = 1029384² - 485485² = 997980² - 414763² is the difference of 2 nonnegative squares in 8 ways.
823935734231 is the difference of 2 positive pentagonal numbers in 8 ways.
823935734231 is not the sum of 3 positive squares.
823935734231² = 480361262719² + 669420011220² = 843501444² + 823935302465² = 264625606975² + 780284167644² = 361050490281² + 740616390320² = 137612470144² + 812362543575² = 391972609065² + 724725857056² = 272155367556² + 777689880385² = 231473080319² + 790753000140² = 508173688895² + 648559631844² = 360292097535² + 740985626444² = 138444051460² + 812221237569² = 579787989844² + 585419491455² = 479675694505² + 669911428656² is the sum of 2 positive squares in 13 ways.
823935734231² is the sum of 3 positive squares.
823935734231 is a proper divisor of 997²⁹⁶²⁹⁶ - 1.
823935734231 = '82393' + '5734231' is the concatenation of 2 prime numbers.

Number of the day: 4719335

Gaspard Monge was born on this day 273 years ago.

Properties of the number 4719335:

4719335 is a cyclic number.
4719335 = 5 × 179 × 5273 is a sphenic number and squarefree.
4719335 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 3753664 totatives.
4719335 = 2359668² - 2359667² = 471936² - 471931² = 13272² - 13093² = 3084² - 2189² is the difference of 2 nonnegative squares in 4 ways.
4719335 is the difference of 2 positive pentagonal numbers in 3 ways.
4719335 is not the sum of 3 positive squares.
4719335² = 3315975² + 3358040² = 637956² + 4676017² = 696847² + 4667604² = 2831601² + 3775468² is the sum of 2 positive squares in 4 ways.
4719335² is the sum of 3 positive squares.
4719335 is a proper divisor of 359²⁶³⁶ - 1.
4719335 = '471' + '9335' is the concatenation of 2 semiprime numbers.

Number of the day: 6440

Properties of the number 6440:

6440 = 2³ × 5 × 7 × 23 is the 5603^th composite number and is not squarefree.
6440 has 4 distinct prime factors, 32 divisors, 19 antidivisors and 2112 totatives.
6440 has a semiprime digit sum 14 in base 10.
6440 = (20 × 21)/2 + … + (35 × 36)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6440 = 1611² - 1609² = 807² - 803² = 327² - 317² = 237² - 223² = 171² - 151² = 129² - 101² = 93² - 47² = 81² - 11² is the difference of 2 nonnegative squares in 8 ways.
6440 is the difference of 2 positive pentagonal numbers in 3 ways.
6440 = 10² + 16² + 78² is the sum of 3 positive squares.
6440² = 3864² + 5152² is the sum of 2 positive squares in 1 way.
6440² is the sum of 3 positive squares.
6440 is a proper divisor of 139² - 1.
6440 is palindromic in (at least) the following bases: 21, 33, 41, 91, -19, -39, -58, and -74.
6440 in base 3 = 22211112 and consists of only the digits '1' and '2'.
6440 in base 12 = 3888 and consists of only the digits '3' and '8'.
6440 in base 21 = ece and consists of only the digits 'c' and 'e'.
6440 in base 33 = 5u5 and consists of only the digits '5' and 'u'.
6440 in base 41 = 3Y3 and consists of only the digits '3' and 'Y'.

The number 6440 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007742: a(n) = n*(4*n+1).
A033587: a(n) = 2*n*(4*n + 3).
A045944: Rhombic matchstick numbers: a(n) = n*(3*n+2).
A078355: Minimal (positive) solution a(n) of Pell equation b(n)^2 - D(n)*a(n)^2 = +4 with D(n)= A077425(n). The companion sequence is a(n)=A077428(n).
A085146: Numbers n such that n!!!!+1 is prime.
A163934: Triangle related to the asymptotic expansion of E(x,m=4,n).
A175525: Numbers n such that n divides the sum of digits of 13^n.
A196856: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,0,2,4 for x=0,1,2,3,4
A234140: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9
A304638: a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 1/x^m)^m for n > 0.

Number of the day: 120544

Properties of the number 120544:

120544 = 2⁵ × 3767 is the 109201^th composite number and is not squarefree.
120544 has 2 distinct prime factors, 12 divisors, 17 antidivisors and 60256 totatives.
Reversing the decimal digits of 120544 results in a prime.
120544 = 30137² - 30135² = 15070² - 15066² = 7538² - 7530² = 3775² - 3759² is the difference of 2 nonnegative squares in 4 ways.
120544 is the difference of 2 positive pentagonal numbers in 2 ways.
120544 = 132² + 204² + 248² is the sum of 3 positive squares.
120544² is the sum of 3 positive squares.
120544 is a proper divisor of 743²⁸ - 1.
120544 is palindromic in (at least) the following bases: 55, and -66.
120544 in base 55 = dkd and consists of only the digits 'd' and 'k'.

The number 120544 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A213586: Antidiagonal sums of the convolution array A213584.

Number of the day: 7735

André Weil was born on this day 113 years ago.

Properties of the number 7735:

7735 is a cyclic number.
7735 = 5 × 7 × 13 × 17 is the 6753^th composite number and is squarefree.
7735 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 4608 totatives.
7735 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 7735 results in a semiprime.
7735 = (26 × 27)/2 + … + (39 × 40)/2 = (6 × 7)/2 + … + (35 × 36)/2 is the sum of at least 2 consecutive triangular numbers in 2 ways.
7735 = 3868² - 3867² = 776² - 771² = 556² - 549² = 304² - 291² = 236² - 219² = 128² - 93² = 92² - 27² = 88² - 3² is the difference of 2 nonnegative squares in 8 ways.
7735 is the sum of 2 positive triangular numbers.
7735 is the difference of 2 positive pentagonal numbers in 6 ways.
7735 is not the sum of 3 positive squares.
7735² = 3640² + 6825² = 1183² + 7644² = 3276² + 7007² = 4032² + 6601² = 735² + 7700² = 5208² + 5719² = 4900² + 5985² = 329² + 7728² = 1848² + 7511² = 2975² + 7140² = 1904² + 7497² = 3927² + 6664² = 4641² + 6188² is the sum of 2 positive squares in 13 ways.
7735² is the sum of 3 positive squares.
7735 is a proper divisor of 1429² - 1.
7735 = '773' + '5' is the concatenation of 2 prime numbers.
7735 = '77' + '35' is the concatenation of 2 semiprime numbers.
7735 is palindromic in (at least) base 90.
7735 in base 23 = ee7 and consists of only the digits '7' and 'e'.
7735 in base 26 = bbd and consists of only the digits 'b' and 'd'.

The number 7735 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A032164: Number of aperiodic necklaces of n beads of 6 colors; dimensions of free Lie algebras.
A074650: Table T(n,k) read by downward antidiagonals: number of Lyndon words (aperiodic necklaces) with n beads of k colors, n >= 1, k >= 1.
A075147: Number of Lyndon words (aperiodic necklaces) with n beads of n colors.
A097102: Numbers n that are the hypotenuse of exactly 13 distinct integer-sided right triangles, i.e., n^2 can be written as a sum of two squares in 13 ways.
A116522: a(0)=1, a(1)=1, a(n)=7a(n/2) for n=2,4,6,..., a(n)=6a((n-1)/2)+a((n+1)/2) for n=3,5,7,....
A143325: Table T(n,k) by antidiagonals. T(n,k) is the number of length n primitive (=aperiodic or period n) k-ary words (n,k >= 1) which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A221578: A sum over partitions (q=6), see first comment.
A271580: Magic sums of 4 X 4 magic squares composed of squares.
A324315: Squarefree integers m > 1 such that if prime p divides m, then the sum of the base p digits of m is at least p.

Number of the day: 931330

Properties of the number 931330:

931330 = 2 × 5 × 93133 is a sphenic number and squarefree.
931330 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 372528 totatives.
931330 has a prime digit sum 19 in base 10.
931330 is the difference of 2 positive pentagonal numbers in 2 ways.
931330 = 611² + 747² = 231² + 937² is the sum of 2 positive squares in 2 ways.
931330 = 192² + 215² + 921² is the sum of 3 positive squares.
931330² = 558798² + 745064² = 184688² + 912834² = 432894² + 824608² = 399950² + 841080² is the sum of 2 positive squares in 4 ways.
931330² is the sum of 3 positive squares.
931330 is a proper divisor of 1361¹¹⁷ - 1.

Number of the day: 7909655

Properties of the number 7909655:

7909655 is a cyclic number.
7909655 = 5 × 13 × 121687 is a sphenic number and squarefree.
7909655 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 5840928 totatives.
7909655 has a prime digit sum 41 in base 10.
Reversing the decimal digits of 7909655 results in a semiprime.
7909655 = 3954828² - 3954827² = 790968² - 790963² = 304224² - 304211² = 60876² - 60811² is the difference of 2 nonnegative squares in 4 ways.
7909655 is the difference of 2 positive pentagonal numbers in 4 ways.
7909655 is not the sum of 3 positive squares.
7909655² = 4745793² + 6327724² = 1946992² + 7666281² = 4015671² + 6814472² = 3042175² + 7301220² is the sum of 2 positive squares in 4 ways.
7909655² is the sum of 3 positive squares.
7909655 is a proper divisor of 1951¹¹⁹³ - 1.
7909655 = '7909' + '655' is the concatenation of 2 semiprime numbers.

Number of the day: 30930

Properties of the number 30930:

30930 = 2 × 3 × 5 × 1031 is the 27596^th composite number and is squarefree.
30930 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 8240 totatives.
30930 has an emirpimes digit sum 15 in base 10.
30930 has a triangular digit sum 15 in base 10.
30930 is the difference of 2 positive pentagonal numbers in 2 ways.
30930 = 4² + 55² + 167² is the sum of 3 positive squares.
30930² = 18558² + 24744² is the sum of 2 positive squares in 1 way.
30930² is the sum of 3 positive squares.
30930 is a proper divisor of 619¹⁰ - 1.
30930 = '30' + '930' is the concatenation of 2 oblong numbers.
30930 is palindromic in (at least) the following bases: 35, 45, -42, and -94.
30930 in base 35 = p8p and consists of only the digits '8' and 'p'.
30930 in base 41 = IGG and consists of only the digits 'G' and 'I'.
30930 in base 44 = Fgg and consists of only the digits 'F' and 'g'.
30930 in base 45 = FCF and consists of only the digits 'C' and 'F'.

The number 30930 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A064262: Values of m such that N=(am+1)(bm+1)(cm+1) is a Carmichael number, where a,b,c = 1,2,51.
A085467: Numerators of coefficients of e^2 in the table of (2n)th du Bois Reymond constants.
A138729: a(n) = -A085466(n) times the free coefficient of the 2n-th Du Bois-Reymond polynomial in e^2.
A214753: Number T(n,k) of solid standard Young tableaux of n cells and height = k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A223034: Number of 3-vexillary permutations in S_n, that is, permutations whose Stanley symmetric function has at most 3 terms or at most 3 Edelman-Greene tableaux.
A273582: Number of solid standard Young tableaux of n cells and height two.

Number of the day: 5866671398

Properties of the number 5866671398:

5866671398 = 2 × 7 × 113 × 347 × 10687 is the 5593050761^th composite number and is squarefree.
5866671398 has 5 distinct prime factors, 32 divisors, 67 antidivisors and 2484623232 totatives.
5866671398 has a prime digit sum 59 in base 10.
Reversing the decimal digits of 5866671398 results in a sphenic number.
5866671398 is the difference of 2 positive pentagonal numbers in 8 ways.
5866671398 = 286² + 639² + 76591² is the sum of 3 positive squares.
5866671398² = 778761690² + 5814753952² is the sum of 2 positive squares in 1 way.
5866671398² is the sum of 3 positive squares.
5866671398 is a proper divisor of 1861¹⁸⁸⁹¹⁶ - 1.

Number of the day: 838704

Properties of the number 838704:

838704 = 2⁴ × 3 × 101 × 173 is the 771907^th composite number and is not squarefree.
838704 has 4 distinct prime factors, 40 divisors, 15 antidivisors and 275200 totatives.
838704 has a sphenic digit sum 30 in base 10.
838704 has an oblong digit sum 30 in base 10.
838704 is the difference of 2 nonnegative squares in 12 ways.
838704 is the difference of 2 positive pentagonal numbers in 1 way.
838704 = 148² + 188² + 884² is the sum of 3 positive squares.
838704² = 405504² + 734160² = 166080² + 822096² = 88704² + 834000² = 252096² + 799920² is the sum of 2 positive squares in 4 ways.
838704² is the sum of 3 positive squares.
838704 is a proper divisor of 347²⁰ - 1.
838704 in base 4 = 3030300300 and consists of only the digits '0' and '3'.

The number 838704 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A286879: Number of minimal dominating sets in the n-Andrasfai graph.

Number of the day: 28347

Carl Friedrich Gauss was born on this day 242 years ago.

Claude Shannon was born on this day 103 years ago.

Properties of the number 28347:

28347 = 3 × 11 × 859 is a sphenic number and squarefree.
28347 has 3 distinct prime factors, 8 divisors, 31 antidivisors and 17160 totatives.
28347 = 14174² - 14173² = 4726² - 4723² = 1294² - 1283² = 446² - 413² is the difference of 2 nonnegative squares in 4 ways.
28347 is the sum of 2 positive triangular numbers.
28347 is the difference of 2 positive pentagonal numbers in 2 ways.
28347 = 13² + 17² + 167² is the sum of 3 positive squares.
28347² is the sum of 3 positive squares.
28347 is a proper divisor of 1979⁶ - 1.
28347 = '283' + '47' is the concatenation of 2 prime numbers.
28347 is palindromic in (at least) the following bases: 2, 32, 41, 67, 74, -34, and -65.
28347 in base 32 = rlr and consists of only the digits 'l' and 'r'.
28347 in base 41 = GZG and consists of only the digits 'G' and 'Z'.
28347 in base 59 = 88R and consists of only the digits '8' and 'R'.

The number 28347 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023609: Convolution of Fibonacci numbers and composite numbers.
A047661: Row 5 of square array defined in A047662.
A066897: Total number of odd parts in all partitions of n.
A270694: Alternating sum of centered heptagonal pyramidal numbers.

Number of the day: 999541962

Henri Poincaré was born on this day 165 years ago.

Properties of the number 999541962:

999541962 = 2 × 3² × 17 × 3266477 is the 948716359^th composite number and is not squarefree.
999541962 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 313581696 totatives.
999541962 = 209³ + 393³ + 976³ is the sum of 3 positive cubes in 1 way.
999541962 is the difference of 2 positive pentagonal numbers in 2 ways.
999541962 = 16629² + 26889² = 2019² + 31551² is the sum of 2 positive squares in 2 ways.
999541962 = 59² + 640² + 31609² is the sum of 3 positive squares.
999541962² = 470372688² + 881948790² = 127402938² + 991389240² = 446494680² + 894274362² = 578950470² + 814800888² is the sum of 2 positive squares in 4 ways.
999541962² is the sum of 3 positive squares.
999541962 is a proper divisor of 179¹¹⁰⁷²⁸ - 1.
999541962 = '9995' + '41962' is the concatenation of 2 emirpimes.