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.